Inclusion Criteria:

* SCREENING/PRE-SCREENING REGISTRATION:
* Patients must have pathologically proven squamous cell carcinoma (SCCA) cancer of the lung confirmed by tumor biopsy and/or fine-needle aspiration; disease must be stage IV SCCA, or recurrent; the primary diagnosis of SCCA should be established using the current World Health Organization (WHO)/International Association for the Study of Lung Cancer (IASLC)-classification of Thoracic Malignancies; the diagnosis is based on hematoxylin and eosin (H\&E) stained slides with or without specific defined immunohistochemistry (IHC) characteristic (p40/p63 positive, transcription termination factor \[TTF1\] negative) if required for diagnosis; mixed histologies are not allowed
* Patients must either be eligible to be screened at progression on prior treatment or to be pre-screened prior to progression on current treatment; patients will either consent to the screening consent or the pre-screening consent, not both; these criteria are:

* Screening at progression on prior treatment: to be eligible for screening at progression, patients must have received at least one line of systemic therapy for any stage of disease (stages I-IV) and must have progressed during or following their most recent line of therapy; for patients whose prior systemic therapy was for stage I-III disease only (i.e. patient has not received any treatment for stage IV or recurrent disease), the prior systemic therapy must have been a platinum-based chemotherapy regimen and disease progression on the platinum-based chemotherapy must have occurred within one year from the last date that patient received that therapy; for patients whose prior therapy was for stage IV or recurrent disease, the patient must have received at least one line of a platinum-based chemotherapy regimen or checkpoint inhibitor therapy (e.g. nivolumab or pembrolizumab)
* Pre-screening prior to progression on current treatment: to be eligible for pre-screening, current treatment must be for stage IV or recurrent disease and patient must have received at least one dose of the current regimen; patients must have previously received or currently be receiving a platinum-based chemotherapy regimen or checkpoint inhibitor therapy (e.g. nivolumab or pembrolizumab); patients on first-line platinum-based treatment are eligible upon receiving cycle 1, day 1 infusion; Note: patients will not receive their sub-study assignment until they progress and the S1400 Notice of Progression is submitted
* Patients must have adequate tumor tissue available, defined as >= 20% tumor cells and >= 0.2 mm\^3 tumor volume

* The local interpreting pathologist must review the specimen
* The pathologist must sign the S1400 Local Pathology Review Form confirming tissue adequacy prior to screening/pre-screening registration
* Patients must agree to have this tissue submitted to Foundation Medicine for common broad platform Clinical Laboratory Improvement Act (CLIA) biomarker profiling; if archival tumor material is exhausted, then a new fresh tumor biopsy that is formalin-fixed and paraffin-embedded (FFPE) must be obtained; a tumor block or FFPE slides 4-5 microns thick must be submitted; bone biopsies are not allowed; if FFPE slides are to be submitted, at least 12 unstained slides plus an H\&E stained slide, or 13 unstained slides must be submitted; however it is strongly recommended that 20 FFPE slides be submitted; Note: previous next-generation deoxyribonucleic acid (DNA) sequencing (NGS) will be repeated if done outside this study for sub-study assignment; patients must agree to have any tissue that remains after NGS testing retained for the use of the translational medicine (TM) studies (if such TM studies are defined) within any sub-study the patient is enrolled in
* Patients must not have a known epidermal growth factor receptor (EGFR) mutation or anaplastic lymphoma kinase (ALK) fusion; EGFR/ALK testing is not required prior to registration and is included in the Foundation Medicine Incorporated (FMI) testing for screening/prescreening
* Patients must have Zubrod performance status 0-1 documented within 28 days prior to screening/pre-screening registration
* Patients must also be offered participation in banking for future use of specimens
* Patients must be willing to provide prior smoking history as required on the S1400 Onstudy Form
* As a part of the Oncology Patient Enrollment Network (OPEN) registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system
* Patients must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines
* SUB-STUDY REGISTRATION:
* Patients whose biomarker profiling results indicate the presence of an EGFR mutation or echinoderm microtubule-associated protein-like 4 (EML4)/ALK fusion are not eligible
* Patients must have progressed (in the opinion of the treating investigator) following the most recent line of therapy
* Patients must not have received any prior systemic therapy (systemic chemotherapy, immunotherapy or investigational drug) within 21 days prior to sub-study registration; patients must have recovered (=< grade 1) from any side effects of prior therapy; patients must not have received any radiation therapy within 14 days prior to sub-study registration
* Patients must have measurable disease documented by computed tomography (CT) or magnetic resonance imaging (MRI); the CT from a combined positron emission tomography (PET)/CT may be used to document only non-measurable disease unless it is of diagnostic quality; measurable disease must be assessed within 28 days prior to sub-study registration; pleural effusions, ascites and laboratory parameters are not acceptable as the only evidence of disease; non-measurable disease must be assessed within 42 days prior to sub-study registration; all disease must be assessed and documented on the Baseline Tumor Assessment Form; patients whose only measurable disease is within a previous radiation therapy port must demonstrate clearly progressive disease (in the opinion of the treating investigator) prior to registration
* Patients must have a CT or MRI scan of the brain to evaluate for central nervous system (CNS) disease within 42 days prior to sub-study registration; patient must not have leptomeningeal disease, spinal cord compression or brain metastases unless: (1) metastases have been locally treated and have remained clinically controlled and asymptomatic for at least 14 days following treatment and prior to registration, AND (2) patient has no residual neurological dysfunction and has been off corticosteroids for at least 24 hours prior to sub-study registration
* Patient must have fully recovered from the effects of prior surgery at least 14 days prior to sub-study registration
* Patients must not be planning to receive any concurrent chemotherapy, immunotherapy, biologic or hormonal therapy for cancer treatment; concurrent use of hormones for non-cancer-related conditions (e.g., insulin for diabetes and hormone replacement therapy) is acceptable
* Absolute neutrophil count (ANC) >= 1,500/mcl obtained within 28 days prior to sub-study registration
* Platelet count >= 100,000 mcl obtained within 28 days prior to sub-study registration
* Hemoglobin >= 9 g/dL obtained within 28 days prior to sub-study registration
* Serum bilirubin =< institutional upper limit of normal (IULN) within 28 days prior to sub-study registration; for patients with liver metastases, bilirubin must be =< 5 x IULN
* Either alanine aminotransferase (ALT) or aspartate aminotransferase (AST) =< 2 x IULN within 28 days prior to sub-study registration (if both ALT and AST are done, both must be =< 2 IULN); for patients with liver metastases, either ALT or AST must be =< 5 x IULN (if both ALT and AST are done, both must be =< 5 x IULN)
* Serum creatinine =< the IULN OR measured or calculated creatinine clearance >= 50 mL/min using the following Cockcroft-Gault Formula within 28 days prior to sub-study registration
* Patients must have Zubrod performance status 0-1 documented within 28 days prior to sub-study registration
* Patients must not have any grade III/IV cardiac disease as defined by the New York Heart Association Criteria (i.e., patients with cardiac disease resulting in marked limitation of physical activity or resulting in inability to carry on any physical activity without discomfort), unstable angina pectoris, and myocardial infarction within 6 months, or serious uncontrolled cardiac arrhythmia
* Patients must not have documented evidence of acute hepatitis or have an active or uncontrolled infection
* Patients with a known history of human immunodeficiency virus (HIV) seropositivity:

* Must have undetectable viral load using standard HIV assays in clinical practice
* Must have cluster of differentiation (CD)4 count >= 400/mcL
* Must not require prophylaxis for any opportunistic infections (i.e., fungal, Mycobacterium avium complex \[mAC\], or pneumocystis jiroveci pneumonia \[PCP\] prophylaxis)
* Must not be newly diagnosed within 12 months prior to sub-study registration
* Prestudy history and physical exam must be obtained within 28 days prior to sub-study registration
* No other prior malignancy is allowed except for the following: adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, adequately treated stage I or II cancer from which the patient is currently in complete remission, or any other cancer from which the patient has been disease free for five years
* Patients must not be pregnant or nursing; women/men of reproductive potential must have agreed to use an effective contraceptive method; a woman is considered to be of "reproductive potential" if she has had menses at any time in the preceding 12 consecutive months; in addition to routine contraceptive methods, "effective contraception" also includes heterosexual celibacy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) defined as a hysterectomy, bilateral oophorectomy or bilateral tubal ligation; however, if at any point a previously celibate patient chooses to become heterosexually active during the time period for use of contraceptive measures outlined in the protocol, he/she is responsible for beginning contraceptive measures
* As part of the OPEN registration process the treating institution?s identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered into the system
* Patients with impaired decision-making capacity are eligible as long as their neurological or psychological condition does not preclude their safe participation in the study (e.g., tracking pill consumption and reporting adverse events to the investigator)
* Patients must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines.