Durvalumab and Lurbinectedin for the Treatment of Relapsed or Refractory Small Cell Lung Cancer

Inclusion Criteria: * Age \>= 18 years * Histological or cytological confirmation of small cell lung cancer * Prior treatment requirements: * Relapsed or progressed after only one prior chemotherapy and PD-1 or PD-L1 inhibitor regimen * Prior therapy must have been an etoposide platinum doublet combined with PD-1 or PD-L1 inhibitor * Group 1: Must have "platinum-sensitive" disease according to the following definitions: * "Sensitive" disease: Relapse occurred \> 90 days after completion of prior therapy * "Resistant" Disease: Relapse occurred =\< 90 days after completion of prior therapy * Group 2: May have "platinum sensitive" (Group 2A) or "platinum resistant" (Group 2B) disease * Measurable disease * Body weight \> 30 kg * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0 or 1 * Hemoglobin \>= 9.0 g/dL (obtained =\< 15 days prior to registration) * Absolute neutrophil count (ANC) \>= 1500/mm\^3 (obtained =\< 15 days prior to registration) * Platelet count \>= 100,000/mm\^3 (obtained =\< 15 days prior to registration) * Albumin \>= 2.5 mg/dL (obtained =\< 15 days prior to registration) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) or direct bilirubin =\< ULN if total bilirubin is \> 1.5 x ULN (obtained =\< 15 days prior to registration) * Alanine aminotransferase (ALT) and aspartate transaminase (AST) =\< 2.5 x ULN (=\< 5 x ULN for patients with liver involvement) (obtained =\< 15 days prior to registration) * Creatinine OR glomerular filtration rate (GFR) =\< 1.5 x ULN OR glomerular filtration rate (GFR) \> 60 mL/min for patients with creatinine \> 1.5 x ULN (obtained =\< 15 days prior to registration) * Negative pregnancy test done =\< 7 days prior to registration, for persons of childbearing potential only * Persons able to become pregnant OR able to father a child must be willing to use an adequate method of contraception while on treatment and for 120 days after last treatment * Life expectancy \>= 12 weeks * Provide written informed consent * Willingness to provide mandatory blood specimens for correlative research * Willingness to provide mandatory tissue specimens for correlative research * Willing to return to Mayo Clinic for follow-up (during the active monitoring phase of the study) Exclusion Criteria: * Any of the following because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown: * Pregnant persons * Nursing persons * Persons of childbearing potential OR able to father a child who are unwilling to employ adequate contraception * Any of the following prior therapies: * Live vaccine \< 30 days prior to registration, including intranasal flu vaccine (e.g. Flu-Mist\[R\]) (Note: Injected seasonal influenza vaccine is not "live") * Surgery \< 28 days prior to registration * Chemotherapy or targeted small molecule therapy \< 21 days prior to registration * Radiation therapy \< 21 days prior to registration * Investigational therapy or investigational device \< 14 days prior to registration * Failure to recover to =\< grade 1 (or baseline) from adverse events due to previously administered therapies or prior surgery. Exceptions: Neuropathy, fatigue, and/or alopecia may be grade 1 * Known active central nervous system (CNS) metastases. NOTE: Patients with previously treated brain metastases may participate provided all of the following are true: * They are stable (without evidence of progression by imaging =\< 4 weeks prior to registration and any neurologic symptoms have returned to baseline) * Have no evidence of new or enlarging brain metastases, and * Are not using steroids =\< 14 days prior to registration * Known leptomeningeal disease * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens * Known active human immunodeficiency virus (HIV) infection (defined as patients who are not on anti-retroviral treatment and have detectable viral load and CD4+ \< 500/ml). NOTE: HIV-positive patients who are well controlled on anti-retroviral therapy are allowed to enroll * Active autoimmune disease requiring systemic treatment, documented history of severe autoimmune disease, or a syndrome that requires systemic steroids or immunosuppressive agents. NOTE: Exceptions are allowed for: * Vitiligo * Resolved childhood asthma/atopy * Intermittent use of bronchodilators or inhaled steroids * Daily steroids at dose of =\< 10mg of prednisone (or equivalent) * Local steroid injections * Stable hypothyroidism on replacement therapy * Stable diabetes mellitus on non-insulin therapy * Sjogren's syndrome * Current or prior use of immunosuppressive medication \< 14 days prior to registration. The following are exceptions to this criterion: * Intranasal, inhaled, topical steroids, or local steroid injections (e.g., intraarticular injection) * Systemic corticosteroids at physiologic doses not to exceed 10 mg/day of prednisone or its equivalent * Steroids as premedication for hypersensitivity reactions (e.g., premedication for computed tomography \[CT\] scans) * Uncontrolled intercurrent illness including, but not limited to: * Ongoing or active infection requiring systemic therapy * Interstitial lung disease * Serious, chronic gastrointestinal conditions associated with diarrhea (e.g., Crohn's disease or others) * Known active hepatitis B (i.e., known positive hepatitis B virus \[HBV\] surface antigen \[HBsAg\] reactive) * Known active hepatitis C (i.e., positive for hepatitis C virus ribonucleic acid \[HCV RNA\] detected by polymerase chain reaction \[PCR\]) * Known active tuberculosis (TB) * Symptomatic congestive heart failure * Unstable angina pectoris * Unstable cardiac arrhythmia or * Psychiatric illness/social situations that would limit compliance with study requirements (e.g., substance abuse) * History of myocardial infarction =\< 6 months, or congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias * Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm * Hypersensitivity to durvalumab or any of its excipients * Previous adverse event attributed to durvalumab or other PD-1 or PD-L1 directed therapy that led to drug discontinuation * History of grade \>= 3 immune-related adverse event or any grade of immune-related neurologic or ocular adverse event while receiving immunotherapy. Note: Patients who had endocrine adverse events =\< grade 2 are allowed to enroll if they are stable on appropriate replacement therapy and asymptomatic * Other active malignancy \< 6 months prior to registration. EXCEPTIONS: Non-melanotic skin cancer, papillary thyroid cancer, or carcinoma-in-situ of the cervix, or others curatively treated and now considered to be at less than 30% risk of relapse