Inclusion Criteria:

* Signed written informed consent obtained prior to study procedures
* Histologically-confirmed relapsed or refractory CD20+ B-cell lymphoma of one of the following types, with documented disease progression or recurrence following the immediate prior therapy:

* DLBCL, regardless of cell of origin or underlying molecular genetics
* MCL
* PMBCL
* Gr3b-FL
* TH-FL
* Biopsy-confirmed CD20+ expression of the underlying malignancy by immunohistochemical staining or flow cytometry between the most recent dose of an anti-CD20 monoclonal antibody (mAb) and study enrollment
* At least 1 measurable lesion on imaging. Lesions that have been previously irradiated will be considered measurable only if progression has been documented following completion of radiation therapy
* Must have received adequate prior therapy for the underlying CD20+ B-cell lymphoma, defined as an anti-CD20 mAb in combination with an anthracycline-containing chemotherapy regimen (i.e. chemo-immunotherapy) and at least one of the following:

* biopsy-proven refractory disease after frontline chemo-immunotherapy
* relapse within 1 year from frontline chemo-immunotherapy and ineligible for autologous hematopoietic stem cell transplant (auto-HSCT)
* For subjects with DLBCL, PMBCL, and Gr3b-FL: relapsed or refractory disease following at least 2 prior regimens or following an auto-HSCT
* For subjects with TH-FL: relapsed or refractory disease following at least 2 prior regimens or following an auto-HSCT. At least 1 prior regimen with an anti-CD20 mAb in combination with chemotherapy is required following documented transformation
* For subjects with MCL (confirmed with cyclin D1 expression or evidence of t(11;14) by cytogenetics, fluorescent in situ hybridization (FISH) or PCR): relapsed or refractory disease after at least 1 prior regimen with chemo-immunotherapy (prior auto-HSCT is allowable)
* Karnofsky performance scale ≥ 60%
* Life expectancy of at least 6 months
* ANC \> 1000/µL
* Platelet count \> 50,000/µL
* For women of childbearing potential (defined as physiologically capable of becoming pregnant), agreement to use of highly effective contraception for at least 1 year following ACTR087 infusion. For men with partners of childbearing potential, agreement to use effective barrier contraception for at least 1 year following ACTR087 infusion

Exclusion Criteria:

* Known active central nervous system (CNS) involvement by malignancy. Subjects with prior CNS involvement with their lymphoma must have completed effective treatment of their CNS disease at least 3 months prior to enrollment with no evidence of disease clinically and at least stable findings on relevant CNS imaging
* Prior treatment as follows:

* alemtuzumab within 6 months of enrollment
* fludarabine, cladribine, or clofarabine within 3 months of enrollment
* external beam radiation within 2 weeks of enrollment
* mAb (including rituximab) within 2 weeks of enrollment
* other lymphotoxic chemotherapy (including steroids except as below) within 2 weeks of enrollment
* experimental agents within 3 half-lives prior to enrollment, unless progression is documented on therapy
* Serum creatinine ≥ 1.5 X age-adjusted upper limits of normal (ULN)
* Pulse oximetry \< 92% on room air
* Direct bilirubin ≥ 3.0 mg/dL (50 mmol/L)
* Alanine transaminase (ALT) ≥ 3 times the ULN, unless determined to be directly due to lymphoma.
* Aspartate transaminase (AST) ≥ 3 times the ULN, unless determined to be directly due to lymphoma
* Class III or IV heart failure as defined by the New York Heart Association (NYHA), history of cardiac angioplasty or stenting, documented myocardial infarction or unstable angina within 6 months prior to enrollment, cardiac ejection fraction of \< 45%, or other clinically significant cardiac disease
* Clinical history of, prior diagnosis of, or overt evidence of autoimmune disease, regardless of severity
* Clinically significant active infection, in the judgment of the investigator
* Pregnancy (negative serum pregnancy test to be obtained within 6 days prior to enrollment for subjects of childbearing potential)
* Breastfeeding
* Primary immunodeficiency
* Seropositive for Human Immunodeficiency Virus (HIV) 1 or HIV 2, or positive hepatitis B surface antigen (HBsAg) or hepatitis C antibody
* Will need or has needed active treatment of a second malignancy within the prior 3 years before enrollment, other than FL, non-melanoma skin cancers, localized prostate cancer treated with curative intent, or cervical carcinoma in situ
* Is unable to receive any of the agents used in this study due a history of severe immediate hypersensitivity reaction (e.g. hypersensitivity to dimethyl sulfoxide (DMSO))
* History of prior allogeneic HSCT
* History of Richter's transformation from CLL
* Prior infusion of a genetically modified therapy