Testing of Tazemetostat in Combination With Topotecan and Pembrolizumab in Patients With Recurrent Small Cell Lung Cancer

Inclusion Criteria: * Patients enrolled to the primary cohort must have limited- or extensive-disease SCLC at diagnosis, with relapse at study entry with measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1, and with prior therapy with platinum doublet. Patients with extensive stage disease should have received chemo-immunotherapy. Both platinum-sensitive and platinum-resistant patients will be included * Age \>= 18 years. Because no dosing or adverse event data are currently available on the use of pembrolizumab in combination with tazemetostat and topotecan in patients \< 18 years of age, children are excluded from this study * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 70%) * Leukocytes \>= 3000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L * Total bilirubin =\< 1.5 institutional upper limit of normal (ULN) OR direct bilirubin =\< ULN for patients with total bilirubin levels \> 1.5 × ULN * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional ULN * Creatinine =\< 1.5 institutional ULN OR glomerular filtration rate (GFR) \>= 60 mL/min/1.73 m\^2 unless data exists supporting safe use at lower kidney function values, no lower than 30 mL/min/1.73 m\^2 * Note: Creatinine clearance (CrCl) should be calculated per institutional standard. Glomerular filtration rate (GFR) can also be used in place of creatinine or CrCl * International normalized ratio (INR) or prothrombin time (PT) =\< 1.5 × ULN unless patient is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants * Activated (a)PTT =\< 1.5 × ULN unless patient is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load (CD4 count of greater than 250 cells/mcL) within 6 months are eligible for this trial. They must not be receiving prophylactic therapy for an opportunistic infection * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated * Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load * Patients with treated brain metastases are eligible if they are symptomatically stable while off steroid therapy for a minimum of 7 days * Patients should be class 2B or better on the New York Heart Association Functional Classification * Ability to understand and the willingness to sign a written informed consent document * The effects of pembrolizumab and tazemetostat on the developing human fetus are unknown. For this reason and because monoclonal antibodies, EZH2 inhibitors as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study treatment and for 6 months after the last dose of study treatment. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 3 months after completion of study treatment administration Exclusion Criteria: * Patients who have had chemotherapy, immune checkpoint inhibitors, or radiotherapy within 2 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study. * Note: Patients who have had palliative radiotherapy may be included as long as they have recovered from any radiotherapy related adverse events (allow at least 3 days between radiotherapy completion and study treatment) * Patients who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities \> grade 1). * Note: Patients with =\< grade 2 neuropathy or =\< grade 2 alopecia are an exception to this criterion and may qualify for the study * Note: If patients received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy * Untreated immunodeficiency or receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment. The use of physiologic doses of corticosteroids may be approved after consultation with the study principal investigator (PI) * Patients who are receiving any other investigational agents * Patients with symptomatic brain metastasis are not eligible due to their extremely poor prognosis and since it is unclear whether the investigational agent penetrates the blood-brain barrier. However, subjects who have had treatment for their brain metastasis and are symptomatically stable while off steroid therapy for a minimum of 7 days may be enrolled. The use of physiologic doses of corticosteroids may be approved after consultation with the study PI * History of allergic reactions attributed to compounds of similar chemical or biologic composition to pembrolizumab and tazemetostat or other agents used in study * Has an active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease modifying agents, corticosteroids, or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment * Has a history of (non-infectious) pneumonitis that required steroids or current pneumonitis * Patients with uncontrolled intercurrent illness but not limited to, ongoing or active infection, interstitial lung disease or active, non-infectious pneumonitis, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Patients with psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because pembrolizumab as a monoclonal antibody, and tazemetostat as a EZH2 inhibitor may have 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 pembrolizumab or tazemetostat, breastfeeding should be discontinued if the mother is treated with these agents and for 1 week after the last dose of tazemetostat. These potential risks may also apply to other agents used in this study * Has known active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C * Has received a live vaccine within 30 days of planned treatment start. Seasonal flu vaccines that do not contain live virus are permitted * Has thrombocytopenia, neutropenia, or anemia of grade \>= 3 (per Common Terminology Criteria for Adverse Events \[CTCAE\] 5.0 criteria) or any prior history of myeloid malignancies, including myelodysplastic syndrome (MDS) * Has abnormalities known to be associated with MDS (e.g. del 5q, chromosome \[chr\] 7 abnormality \[abn\]) and myeloproliferative neoplasm (MPN) (e.g. JAK2 V617F) observed in cytogenetic testing and DNA sequencing * Has a prior history of T-cell lymphoblastic lymphoma (T-LBL), T-cell acute leukemia (T-ALL) or B-cell acute lymphoblastic leukemia (B-ALL)