Testing the Combination of an Anti-cancer Drug, Iadademstat, With Other Anti-cancer Drugs (Atezolizumab or Durvalumab) at Improving Outcomes for Small Cell Lung Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed small cell lung cancer (SCLC) * Patients who have been treated with platinum etoposide chemotherapy plus either atezolizumab or durvalumab immunotherapy for at least 4 cycles, and no more than 6 cycles, with either a radiographic response or stable disease. Patients are eligible if a maximum of 2 cycles of atezolizumab or durvalumab were omitted with initial treatment * Age ≥ 18 years. Because no dosing or adverse event data are currently available on the use of iadademstat in combination with atezolizumab and durvalumab in patients \<18 years of age, children are excluded from this study * Body weight ≥ 50 kg * Patient is able to swallow oral medications * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 (Karnofsky ≥ 60%). This assessment for eligibility will take place after patients have received 4 cycles of standard of care (SOC) chemotherapy-ICI * Leukocytes ≥ 2,000/mcL * Lymphocyte count ≥ 500/mcL * Absolute neutrophil count ≥ 1,500/mcL * Hemoglobin ≥ 9 g/dL * Platelets ≥ 100,000/mcL * Albumin ≥ 3 g/dL * Total bilirubin ≤ 1.5 institutional upper limit of normal (ULN) * Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\])/ alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) ≤ 3 × institutional ULN unless liver metastases are present, in which case it must be ≤ 5 × ULN * Glomerular filtration rate (GFR) ≥ 45 mL/min * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial * 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 (no escalating steroid use) or asymptomatic, untreated brain metastases (≤ 5 mm without significant edema) are eligible. Brain metastases must not be new after completion of chemotherapy * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * Evidence of post-menopausal status or negative urinary or serum pregnancy test for female pre-menopausal patients. Pregnant women are excluded from this study because atezolizumab and durvalumab are monoclonal antibody agents with the potential for teratogenic or abortifacient effects. Women will be considered post-menopausal if they have been amenorrheic for 12 months without an alternative medical cause. The following age-specific requirements apply: * Women \< 50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of exogenous hormonal treatments and if they have luteinizing hormone and follicle-stimulating hormone levels in the post-menopausal range for the institution or underwent surgical sterilization (bilateral oophorectomy or hysterectomy). * Women ≥ 50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of all exogenous hormonal treatments, had radiation-induced menopause with last menses \>1 year ago, had chemotherapy-induced menopause with last menses \> 1 year ago, or underwent surgical sterilization (bilateral oophorectomy, bilateral salpingectomy or hysterectomy) * The effects of iadademstat, atezolizumab, and durvalumab on the developing human fetus are unknown. For this reason and because monoclonal antibody agents are known to be teratogenic, women of child-bearing potential and males with females of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to registration, for the duration of study participation, and for 150 days after the last dose of study medication. 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. * Females of childbearing potential must agree to: * Use effective contraception during the trial and 150 days after the end of treatment. * Practice true abstinence during the trial and 150 days after the end of treatment. * Have a negative urine pregnancy test at screening. * Not to donate or freeze egg(s) during the course of this study or within 150 days after receiving their last dose of study drug. * Male patients even if surgically sterilized (i.e., status post-vasectomy) must agree to: * Use effective contraception during the entire study treatment period and through 150 days after the last dose of study drug. * Not to donate or freeze sperm during the course of this study or within 150 days after receiving their last dose of study drug. * Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with atezolizumab and durvalumab, female participants who are breastfeeding must agree to discontinue breastfeeding. These potential risks may also apply to iadademstat * Ability to understand and the willingness to sign a written informed consent document. Legally authorized representatives may sign and give informed consent on behalf of study participants Exclusion Criteria: * Patients who receive maintenance ICI therapy prior to cycle 1, day 1 * Patients medicated with anti-depressants reported to have KDM1A/LSD1 inhibitory activity: Tranylcypromine or phenelzine * Patients who have not recovered from grade ≥2 adverse events (AEs) due to prior anti-cancer therapy with the exception of alo