• 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