Lenalidomide and Blinatumomab for the Treatment of Relapsed Non-Hodgkin Lymphoma

Inclusion Criteria:

* Histologically or cytologically confirmed relapsed cluster of differentiation (CD)19+ non-Hodgkin lymphoma (NHL) (included in this category are follicular grade I, II, III, marginal zone, mantle cell, gray zone, primary mediastinal, Burkitt's, diffuse large B cell, small lymphocytic lymphoma); patients previously treated with CD19-targeted therapy (including chimeric antigen receptor T-cells \[CAR T\]) must have a subsequent biopsy and/or flow cytometry confirming CD19 positivity
* Karnofsky \>= 60%
* Life expectancy of greater than 12 weeks
* Absolute neutrophil count \> 1000/mcL
* Platelets \>= 50,000/mcL
* Total bilirubin =\< 1.5 x institutional upper limit of normal
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal
* AST (SGOT)/ALT(SGPT) (only if elevated liver function tests \[LFTs\] are due to disease) =\< 5.0 x institutional upper limit of normal
* Body surface area (BSA)-normalized creatinine clearance \>= 60 mL/min/1.73 m\^2 (using Cockcroft-Gault creatinine clearance \[CrCl\])
* Patients must have had at least two prior chemotherapeutic or biologic (e.g. rituximab alone) regimens and not currently eligible for standard curative options; steroids alone and local radiation do not count as regimens; radiation to \> 1 site and transplant are considered prior regimens
* Any prior therapy must have been completed at least 4 weeks prior to entry into the study
* Females of childbearing potential (FCBP) must have a negative serum or urine pregnancy test with a sensitivity of at least 25 mIU/mL within 10 - 14 days prior to and again within 24 hours of starting lenalidomide and must either commit to continued abstinence from heterosexual intercourse or begin TWO acceptable methods of birth control, one highly effective method and one additional effective method AT THE SAME TIME, at least 28 days before she starts taking lenalidomide; FCBP must also agree to ongoing pregnancy testing; men must agree to use a latex condom during sexual contact with a FCBP even if they have had a successful vasectomy; all patients must be counseled at a minimum of every 28 days about pregnancy precautions and risks of fetal exposure
* Patients must have radiographically measurable disease; radiographically measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \> 20 mm with conventional techniques or as \> 10 mm with spiral computed tomography (CT) scan; lesions in previously irradiated anatomic areas (external beam radiation) cannot be considered target lesions unless there has been documented growth of those lesions after radiotherapy
* Ability to understand and the willingness to sign a written informed consent document
* Human immunodeficiency virus (HIV) infected patients are eligible provided they meet all the other eligibility criteria of the study in addition to the following:

  * During prior lymphoma therapy, patients must not have experienced documented infections attributed to the HIV+ status
  * No history of non-adherence to cART and willing to adhere to cART while on study
  * Antiretroviral drugs with overlapping or similar toxicity profiles as study agents not allowed:

    * Efavirenz not allowed due to potential central nervous system (CNS) toxicity
    * Stavudine not allowed due to potential neuropathic effects
    * Zidovudine not allowed due to myelosuppressive effects
  * Patients must be willing to be followed at a minimum of approximately every 3 months by physician expert in HIV disease management
* Patients must be willing to be followed at a minimum of approximately every 3 months by physician expert in HIV disease management

Exclusion Criteria:

* Patients who have had chemotherapy or radiotherapy within 4 weeks prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier
* Patients who are receiving any other investigational agents
* Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to lenalidomide and blinatumomab or other agents used in study
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
* Pregnant women are excluded from this study because lenalidomide is an agent with the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with lenalidomide, breastfeeding should be discontinued if the mother is treated with lenalidomide
* Concurrent use of other anti-cancer agents or treatments
* Known active hepatitis, type B or C; patients on suppressive therapy with a negative viral load and no evidence of hepatic damage are eligible
* Prior treatment with lenalidomide within 8 weeks prior to entering the study