Lenalidomide, Umbralisib, and Ublituximab for the Treatment of Relapsed or Refractory Indolent Non-Hodgkin Lymphoma or Mantle Cell Lymphoma

Inclusion Criteria: * Documentation of disease at diagnosis and/or relapse (local pathology review is allowed): * Patients in the dose-escalation portion of the study must have histologically confirmed, low-grade B-cell NHL by the World Health Organization (WHO) classification: * Follicular lymphoma (FL) grade 1, 2, or 3a * Marginal zone B-cell lymphoma (MZL), including extranodal, nodal and splenic * Lymphoplasmacytic lymphoma (LPL)/Waldenstrom macroglobulinemia * Mantle cell lymphoma (MCL) * For the expansion cohort, patients must have histologically confirmed FL grade 1, 2, or 3a * Patients with FL or MZL must have had at least one prior systemic therapy. Patients with MCL or LPL/Waldenström macroglobulinemia must have had prior treatment with at least 2 systemic treatments that included a BTK inhibitor (stopped due to progression or intolerance). * Must be in need of treatment for relapsed or refractory disease as assessed by the investigator * Eastern Cooperative Oncology Group (ECOG) performance status 0, 1, or 2 * Patients must have radiographically measurable disease * Patients with LPL/Waldenstrom macroglobulinemia or MZL without radiographically measurable disease may be included if they have a measurable serum monoclonal protein (M protein) * Absolute neutrophil count (ANC) \> 1,000/mcL * Platelet count \> 75,000/mcL * Total bilirubin =\< 1.5 x the upper limit of the normal range (ULN) (unless due to Gilbert's disease) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) \< 2.5 x institutional ULN * Alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) \< 2.5 x institutional ULN * Renal function assessed by calculated creatinine clearance as follows (Cockcroft-Gault estimation of creatinine clearance \[CrCl\]): * Patients in the dose-escalation portion of the study must have calculated creatinine clearance \>= 60 ml/min by Cockcroft-Gault formula * Patients in the expansion cohort must have calculated creatinine clearance \>= 30 ml/min by Cockcroft-Gault formula * Patients on dialysis are not eligible * Participants must agree to ongoing anticoagulation as prophylaxis against deep vein thrombosis (DVT) using aspirin (81 or 325 mg) daily, warfarin or low molecular weight heparin, or a patient already taking another oral anticoagulant (e.g. direct thrombin inhibitors for atrial fibrillation) may continue that agent * All study participants must be registered into the mandatory Revlimid REMS program, and be willing and able to comply with the requirements of the REMS program * A woman of childbearing potential (WOCBP) is a sexually mature female who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 12 consecutive months (i.e., has had menses at any time in the preceding 12 consecutive months) * Female patients who are WOCBP must agree to practice: * Effective methods of contraception, at the same time, from the time of signing the informed consent form through 90 days after the last dose of study drug, OR * True abstinence when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[e.g., calendar, ovulation, symptothermal, post-ovulation methods\] and withdrawal are not acceptable methods of contraception) * A WOCBP must have a negative serum or urine pregnancy test with a sensitivity of at least 50 mIU/mL within 10-14 days prior to and again within 24 hours of starting therapy with Revlimid. Females of reproductive potential must adhere to the scheduled pregnancy testing as required in the Revlimid REMS program * Male patients, even if surgically sterilized (i.e., status post-vasectomy), must agree to one of the following: * Agree to practice effective barrier contraception during the entire study treatment period and through 90 days after the last dose of study drug, OR * Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[e.g., calendar, ovulation, symptothermal, post-ovulation methods\] and withdrawal are not acceptable methods of contraception) * Subjects must have the ability to understand and the willingness to sign a written informed consent document and Health Insurance Portability and Accountability Act (HIPAA) consent document. Voluntary written consent must be given before performance of any study related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the patient at any time without prejudice to future medical care Exclusion Criteria: * Known or suspected active diffuse large B-cell lymphoma (DLBCL). Patients with prior history of DLBCL may be enrolled if their DLBCL has been previously treated and - in the opinion of the investigator - is not active * Patients who have not recovered (i.e., \>= grade 2 toxicity) from adverse events due to agents administered more than 4 weeks earlier, and patients who have any grade pulmonary or related infections thought to be associated with pneumonitis, or any grade colitis * Major surgery within 14 days before day 1, cycle 1 of treatment * Radiotherapy within 14 days before day 1, cycle 1 of treatment * Patients with prior systemic therapy must have had a minimum of 14 days from prior treatment with a BTK inhibitor, or 21 days from prior treatment with chemotherapy or any other therapy and day 1, cycle 1 of treatment. Concurrent glucocorticoid therapy as long as started for at least 7 days prior to study entry (=\< 20 mg per day of prednisone or equivalent) is allowed as clinically warranted * Known central nervous system involvement. Subjects with symptoms of central nervous system (CNS) disease must have a negative computed tomography (CT) scan and negative diagnostic lumbar puncture * Any prior use of lenalidomide * Any prior use of idelalisib (CAL-101), duvelisib (IPI-145), copanlisib or any other drug that specifically inhibits phosphoinositide-3-kinase (PI3K) * Prior allogeneic stem cell transplantation. Prior autologous stem cell transplant is allowed, if it was 6 months or longer ago * Active systemic bacterial, fungal or viral infection except localized fungal infections of skin or nails. Patients with resolving infections such as urinary tract, respiratory, other than a respiratory infection thought to be associated with pneumonitis, or skin infections may be enrolled if clinically improving. NOTE: Subjects may be receiving prophylactic antiviral or antibacterial therapies at investigator discretion. Use of anti-pneumocystis and antiviral prophylaxis is required for subjects receiving umbralisib * Patients with a history of deep vein thrombosis (DVT) or pulmonary embolus (PE) within 3 months before study entry are not eligible. Patients with history of DVT/PE greater than 3 months are eligible but recommended to receive aspirin, molecular weight heparin or direct thrombin inhibitor unless contraindicated * Evidence of current uncontrolled or symptomatic cardiovascular conditions, including, uncontrolled cardiac arrhythmias, history of or symptomatic congestive heart failure (NYHA class II or greater), unstable angina, or myocardial infarction within the past 6 months. Poorly controlled or clinically significant atherosclerotic vascular disease including cerebrovascular accident (CVA), transient ischemic attack (TIA), angioplasty, cardiac or vascular stenting within 6 months of enrollment. Concomitant use of medication known to cause QT prolongation or torsade de pointes should be used with caution and at investigator discretion * .Patients with history of autoimmune hepatitis, autoimmune or drug-induced colitis including inflammatory bowel disease (ulcerative colitis or Crohn's disease), and/or autoimmune or drug-induced pneumonitis * Known history of drug-induced liver injury, alcoholic liver disease, non-alcoholic steatohepatitis, primary biliary cirrhosis, ongoing extrahepatic obstruction caused by stones, or cirrhosis of the liver * Known gastrointestinal (GI) disease or gastrointestinal procedure that will significantly interfere with the oral absorption or tolerance of umbralisib or lenalidomide including inability to swallow pills/capsules * Any serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of treatment according to this protocol * Known allergy to any of the study medications, their analogues, or excipients in the various formulations of any agent. Specifically, prior desquamating rash, erythema nodosum, toxic epidermal necrolysis, or Stevens-Johnson syndrome during prior thalidomide or other similar agents * No evidence of prior malignancy except: DLBCL, adequately treated non-melanoma skin cancer, adequately treated in situ carcinoma, low grade prostate carcinoma (Gleason grade =\< 6) managed with observation that has been stable for at least 6 months, or any malignancy treated with curative intent and continuously disease free for at least 3 years * Ongoing immunosuppressive therapy (such as tacrolimus, cyclosporine, mycophenolate, methotrexate, tumor necrosis factor \[TNF\] inhibitors, alemtuzumab). Systemic corticosteroids (prednisone or equivalent =\< 20 mg daily) are allowed as clinically warranted. Patients are allowed to use topical or inhaled corticosteroids * Participation in other interventional clinical trials, including those with other investigational agents not included in this trial, within 21 days of day 1, cycle 1 of this trial. Also excluded are patients who are receiving any other investigational agents outside of a clinical trial * Evidence of chronic active hepatitis B (hepatitis B virus \[HBV\], not including patients with prior hepatitis B vaccination; or positive serum hepatitis B antibody) or chronic active hepatitis C infection (HCV), active cytomegalovirus (CMV), or known history of human immunodeficiency syndrome (HIV). If hepatitis B core (HBc) antibody is positive, the subject must be evaluated for the presence of HBV deoxyribonucleic acid (DNA) by polymerase chain reaction (PCR). If HCV antibody is positive, the subject must be evaluated for the presence of HCV ribonucleic acid (RNA) by PCR. If the subject is CMV immunoglobulin G (IgG) or CMV IgM positive, the subject must be evaluated for the presence of CMV DNA by PCR. Subjects with positive HBc antibody and negative HBV DNA by PCR are eligible. Subjects with positive HCV antibody and negative HCV RNA by PCR are eligible. Subjects who are CMV IgG or CMV IgM positive but who are CMV DNA negative by PCR are eligible * Pregnant or breastfeeding women are excluded from this study because lenalidomide has known teratogenic 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. These potential risks may also apply to other agents used in this study * History of anaphylaxis (excluding infusion related reactions) in association with previous anti-CD20 administration * Live virus vaccines within 4 weeks prior to ublituximab therapy