Inclusion Criteria:

* ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C) - STEP 0: Patient must be considered a potential candidate for the trial

* NOTE: Enrollment to Step 0 may occur prior to or following completion of the assessments to verify patient eligibility for Step 1 registration; bone marrow and/or peripheral blood specimens collected during Step 0 or prior to treatment on Step 1 must be submitted for central review in order for the patient to be considered evaluable; results will not be reported to the site and will not impact patient participation in the trial
* ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C) - STEP 1: Patients must have a diagnosis of:

* Relapsed or refractory B-cell or T-cell ALL after multi-agent chemotherapy
* Patients with \< 5% blasts may enroll on trial in phase I portion provided that minimal residual disease (MRD) is present at \> 10\^-3 as tested on an assay with minimum sensitivity of 10\^-4 OR
* Relapsed lymphoblastic lymphoma
* ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): Age \>= 18 years
* ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C) - STEP 1: Eastern Cooperative Oncology Group (ECOG) performance status 0-2
* ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C) - STEP 1: Adequate liver function with aspartate aminotransferase (AST)/alanine aminotransferase (ALT) less than 3 x upper limit of normal and total bilirubin less than 2 mg/dL within 10 days prior to first dose of study agent
* ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C) - STEP 1: Circulating white blood cell (WBC) count must not be above 25 x 10\^9/L at the time of registration

* Patients with WBC count above 25 x 10\^9/L are eligible if they have started steroids or hydroxyurea per institutional guidelines
* ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C) - STEP 1: Glomerular filtration rate (GFR) of at least 40 mL/min within 7 days prior to first dose of study agent
* ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C) - STEP 1: All patients of childbearing potential must have a blood test or urine study with a minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin (HCG) within 2 weeks prior to registration to rule out pregnancy

* A patient of childbearing potential is defined as anyone, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy; or 3) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months)
* ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C) - STEP 1: Patients must not expect to conceive or father children by using accepted and highly effective method(s) of contraception or by abstaining from sexual intercourse for the duration of their participation in the study and for 30 days after the last dose of venetoclax

* Should a patient or a partner of a patient become pregnant or suspect they are pregnant while participating in the study, the treating physician should be notified immediately
* ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C) - STEP 1: No evidence of prior solid malignancy except adequately treated non-melanoma skin cancer, in situ cervical carcinoma, or any surgically- or radiation-cured malignancy continuously disease free for \>= 2 years so as not to interfere with interpretation of radiographic response
* ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C) - STEP 1: Patients may be enrolled with a prior allogeneic hematopoietic stem cell transplant (HSCT) but the transplant date must be at least 90 days before date of registration to step 1; patient must be off immunosuppression and without active graft versus host disease (GVHD) prior to registration to step 1 if previous HSCT
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 0: Patient must be considered a potential candidate for the trial

* NOTE: Enrollment to Step 0 may occur prior to or following completion of the assessments to verify patient eligibility for Step 1 registration
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 1: Relapsed or refractory B-cell or T-cell ALL, including lymphoblastic lymphoma, after at least one line of chemotherapy
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 1: Age \>= 18 years
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 1: ECOG performance status 0-2
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 1: Adequate liver function with AST/ALT less than 3 x upper limit of normal and total bilirubin less than 2 mg/dL within 10 days prior to first dose of study agent
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 1: Circulating WBC count must not be above 25 x 10\^9/L at the time of registration to step 1

* Patients with WBC count above 25 x 10\^9/L are eligible if they have started steroids or hydroxyurea per institutional guidelines
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 1: GFR of at least 40 mL/min within 7 days prior to first dose of study agent
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 1: All patients of childbearing potential must have a blood test or urine study with a minimum sensitivity 25 IU/L or equivalent units of HCG within 2 weeks prior to registration to rule out pregnancy.

* A patient of childbearing potential is defined as anyone, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy; or 3) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months)
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 1: Patients must not expect to conceive or father children by using accepted and highly effective method(s) of contraception or by abstaining from sexual intercourse for the duration of their participation in the study and for 30 days after the last dose of venetoclax

* Should a patient or partner of a patient become pregnant or suspect she is pregnant while participating in this study, the treating physician should be informed immediately
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 1: Patients may be enrolled with a prior allogeneic hematopoietic stem cell transplant (HSCT) but the transplant date must be at least 90 days before date of enrollment; patient must be off immunosuppression and without active GVHD prior to enrollment if previous HSCT. Low-dose steroids (10mg or less) are allowed

Exclusion Criteria:

* ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C) - STEP 1: Patients of childbearing potential must not be pregnant or breast-feeding due to risk of fetal harm by the chemotherapeutic agents prescribed in this protocol
* ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C) - STEP 1: Patients with isolated testicular or central nervous system (CNS) relapsed disease are not eligible
* ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C) - STEP 1: Patients must not have Burkitt's lymphoma/leukemia based on the World Health Organization (WHO) criteria
* ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C) - STEP 1: Patients must not have active central nervous system (CNS) leukemia, as defined by unequivocal morphologic evidence of lymphoblasts in the cerebrospinal fluid (CSF) or the use of CNS-directed local treatment for active disease within the prior 28 days; prophylactic intrathecal chemotherapy is allowed; previously treated CNS disease with documented clearance of the CSF will be allowed
* ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C) - STEP 1: Patients will not be enrolled if they received prior chemotherapy within 2 weeks before registration to step 1 with the following exceptions: to reduce the circulating lymphoblast count or palliation or for ALL maintenance (mercaptopurine, methotrexate, vincristine, thioguanine, and/or tyrosine kinase inhibitors)
* ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C) - STEP 1: Patients cannot have poorly controlled chronic viral infections including hepatitis B, C, or human immunodeficiency virus (HIV); HIV positive patients are allowed on this study if they have a CD4 count \>= 400, and are on a stable antiviral regimen
* ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C) - STEP 1: Patients with New York Heart Association (NYHA) class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia may not be enrolled
* ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C) - STEP 1: Patients with serious medical or psychiatric illness that in the opinion of the primary investigator is likely to interfere with study participation may not be enrolled
* ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C) - STEP 1: Patients must not be taking any other experimental medications within 21 days prior to registration. Clinical trial medications that are Food and Drug Administration (FDA) approved will be allowed within 14 days prior to registration
* ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C) - STEP 1: Patients should not have received the following within 7 days prior to the first dose of study drug:

* Strong and moderate CYP3A inhibitors;
* Strong and moderate CYP3A inducers
* ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C) - STEP 1: Patients must not have grade 3 or higher peripheral neuropathy or history of grade 3 or higher peripheral neuropathy. Patients with familial demyelinating disease like Charcot-Marie-Tooth disease are also excluded
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 1: Patients with prior venetoclax treatment for ALL will be excluded
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 1: Patients must not be pregnant or breast-feeding due to risk of fetal harm by the chemotherapeutic agents prescribed in this protocol
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 1: No evidence of prior malignancy except adequately treated non-melanoma skin cancer, in situ cervical or breast carcinoma, or chemotherapy-surgically- or radiation-cured malignancy continuously disease free for \>= 2 years
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 1: Patients with isolated testicular or CNS relapsed disease are not eligible
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 1: Patients must not have Burkitt's lymphoma/leukemia based on the WHO criteria
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 1: Patients must not have active central nervous system (CNS) leukemia, as defined by unequivocal morphologic evidence of lymphoblasts in the cerebrospinal fluid (CSF) or the use of CNS-directed local treatment for active disease within the prior 28 days; prophylactic intrathecal chemotherapy is allowed; previously treated CNS disease with documented clearance of the CSF will be allowed and once cleared, prophylactic intrathecal chemotherapy can be continued
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 1: Patient will not be enrolled if they received prior chemotherapy within 2 weeks before enrollment with the following exceptions: to reduce the circulating lymphoblast count or palliation (i.e., steroids or hydroxyurea), for ALL maintenance (mercaptopurine, methotrexate, vincristine, thioguanine, and/or tyrosine kinase inhibitors)
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 1: Patients cannot have poorly controlled chronic viral infections including hepatitis B, C, or HIV; HIV positive patients with undetectable viral load are allowed
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 1: Patients with NYHA class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia may not be enrolled
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 1: Patients with serious medical or psychiatric illness that in the opinion of the primary investigator is likely to interfere with study participation may not be enrolled
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 1: Patients must not be participating in any other clinical trial or taking any other experimental medications within 21 days prior to registration
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 1: Patients must not have received the following within 7 days prior to the first dose of study drug or while on study treatment:

* Strong and moderate CYP3A inhibitors;
* Strong and moderate CYP3A inducers
* ELIGIBILITY CRITERIA - PHASE II (ARM D) - STEP 1: Patients must not have grade 3 or higher peripheral neuropathy or history of grade 3 peripheral neuropathy; patients with familial demyelinating diseases like Charcot-Marie-Tooth disease also excluded