Obinutuzumab With or Without Umbralisib, Lenalidomide, or Combination Chemotherapy in Treating Patients With Relapsed or Refractory Grade I-IIIa Follicular Lymphoma

Inclusion Criteria: * Patients must have follicular lymphoma (grade I, II or IIIa) confirmed at initial diagnosis and at relapse with identifiable fludeoxyglucose F-18 (FDG) avid disease on PET/CT; patients that have involvement with large cell lymphoma are not eligible * Patients must have a whole body or limited whole body PET/CT scan performed within 42 days prior to registration * Patients must have bone marrow biopsy performed within 42 days prior to registration * Patients must have an indication for therapy as determined by the treating investigator * All disease must be assessed and documented on the S1608 FDG-PET/CT assessment form * The intent is to enroll patients with follicular lymphoma (FL) relapsed within 2 years of completing their first course of chemotherapy (CHOP or bendamustine based therapy) + anti-CD20 therapy. Patient is still eligible if he/she received radiation therapy or anti-CD20 therapy prior to chemoimmunotherapy or if maintenance anti-CD20 therapy was administered after chemoimmunotherapy * Patients must have either failed to achieve a complete remission, or must have relapsed within 2 years after completing CHOP or bendamustine-containing chemoimmunotherapy (including an anti-CD20 monoclonal antibody), as measured from the last dose of CHOP or bendamustine; relapsed patients must not have received any intervening chemotherapy * Patients must have received only 1 course of chemotherapy, containing at least 3 cycles of CHOP or bendamustine; (note that no minimum dose of bendamustine is required) * Patients who received any anti-CD20 antibody therapy prior to CHOP or bendamustine are eligible * Patients who additionally received any maintenance anti-CD-20 antibody therapy or consolidative radioimmunotherapy within 2 years of the last dose of the CHOP or bendamustine therapy are eligible * Involved field or involved site radiation is not considered a line of therapy; examples of eligible prior treatment regimens (note this list is not all inclusive): * 1st line rituximab treatment followed years later by bendamustine rituximab * Bendamustine rituximab x 4 cycles * 1st line rituximab treatment, 2nd line ibritumomab tiuxetan, followed by bendamustine bortezomib rituximab x 6 cycles followed by rituximab maintenance * Bendamustine obinutuzumab x 3 cycles * CHOP rituximab x 6 cycles followed by rituximab maintenance * For all forms of systemic therapy, patients must have completed therapy at least 21 days prior to registration; patients must have completed any radioimmunotherapy at least 84 days prior to registration; patients prior treatment related toxicities (except alopecia) must have resolved to grade 1 or less prior to registration * Patients must have tissue specimens collected prior to registration; patients must be offered participation in biobanking of residual specimens; with patient consent, residuals from the mandatory submission(s) will be banked for future research * Patients must be \>= 18 years of age * All patients must have a Zubrod performance status of 0, 1 or 2 * Absolute neutrophil count (ANC) \>= 1,500/mcL within 28 days prior to registration * Platelets \>= 75,000/mcL within 28 days prior to registration * Patients must have adequate renal function as documented by a calculated creatinine clearance \>= 60 mL/min, within 28 days prior to registration * Total bilirubin =\< 1.5 x institutional upper limit of normal (IULN) (=\< 5 x IULN if secondary to lymphoma, Gilbert's syndrome, or medication related \[e.g., indinavir, tenofovir, atazanavir\]) within 28 days prior to registration * Direct bilirubin =\< 1.5 x IULN (=\< 5 x IULN if secondary to lymphoma) within 28 days prior to registration * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x IULN (=\< 5 x IULN secondary to lymphoma) within 28 days prior to registration * Patients must have an echocardiogram (ECHO) or multigated acquisition (MUGA) scan within 42 days prior to registration with a cardiac ejection fraction \>= 45% * Patients with hepatitis B virus infection must have undetectable hepatitis B virus (HBV) on suppressive therapy and no evidence of HBV-related hepatic damage; patients with hepatitis C virus infection are eligible if complete eradication therapy has been successfully completed, and there is no detectable hepatitis C virus (HVC) or related hepatic damage; patients with known human immunodeficiency virus (HIV) infection are eligible if they meet all of the following criteria in addition to the other protocol eligibility criteria: * Patient must have no history of acquired immune deficiency syndrome (AIDS)-related complications, other than a history of low CD4+ T-cell count (\< 200/mm\^3) prior to initiation of combination antiretroviral therapy; on study CD4+ T-cell count may not be informative due to leukemia and should not be used as an exclusion criterion if low * Patient must be healthy on the basis of HIV disease with high likelihood of near normal life span were it not for the leukemia * Patient must have serum HIV viral load of \< 200 copies/mm\^3 * Patient must be on combination antiretroviral therapy with minimal pharmacokinetic interactions with study therapy and minimal overlapping clinical toxicity with protocol therapy; (recommend a regimen of the integrase inhibitor dolutegravir combined with either disoproxil fumarate/emtricitabine or dolutegravir combined with tenofovir alafenamide/emtricitabine) * Protease inhibitors and once daily formulations containing cobicistat are NOT allowed due to potential pharmacokinetic interactions with leukemia therapy * Stavudine and zidovudine (AZT) are NOT allowed because of overlapping toxicity with protocol therapy * Patients must be able and willing to receive prophylaxis with daily aspirin, low molecular weight heparin, factor X inhibitors or warfarin if randomized to lenalidomide; patients unable or unwilling to take any listed prophylaxis are NOT eligible * No second prior malignancy is allowed except for adequately treated basal (or squamous cell) skin cancer, in situ cervical cancer or other cancer for which the patient has been disease free for three years * Patients must have a complete history and physical examination within 28 days prior to registration * 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 and again within 24 hours prior to starting cycle 1 of lenalidomide; further, they must either commit to complete abstinence (true abstinence is acceptable when this is in line with the preferred and usual lifestyle of the subject; periodic abstinence \[e.g., calendar, ovulation, symptothermal or post ovulation methods\] and withdrawal are not acceptable methods of contraception) 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 starting lenalidomide; while taking lenalidomide, during dose interruptions, and for at least 28 days after the last dose of 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; a FCBP is a female who: 1) has achieved menarche at some point; 2) has not undergone a hysterectomy or bilateral oophorectomy; or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months); all patients must be counseled by a trained counselor every 28 days about pregnancy precautions and risks of fetal exposure; NOTE: patients not randomized to receive lenalidomide will not be required to undergo serial pregnancy testing or lenalidomide counseling after registration * Patients must have lactate dehydrogenase (LDH) and beta-2-microglobulin collected within 28 days prior to registration * 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 * 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 Exclusion Criteria: * Patients must not have clinical evidence of central nervous system involvement by lymphoma since the proposed treatment strategies are not designed to address central nervous system (CNS) involvement adequately; if performed, any laboratory or radiographic tests performed to assess CNS involvement must be negative * Patients must not have any prior treatment with any PI3K inhibitor, or lenalidomide