Testing the Combination of MLN4924 (Pevonedistat), Carboplatin, and Paclitaxel in Patients With Advanced Non-small Cell Lung Cancer (NSCLC) Who Have Previously Been Treated With Immunotherapy

Inclusion Criteria

• •Patients must be \>= 18 years old. Because no dosing or adverse event (AE) data are currently available on the use of MLN4924 (pevonedistat) in combination with carboplatin and paclitaxel in patients \< 18 years of age, children are excluded from this study, but may be eligible for future pediatric trials.
• •Patients must have histologically confirmed stage IIIB or IV NSCLC (squamous or nonsquamous) that is metastatic or unresectable.
• •Patients must have measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1.
• •* Patients who have progressed after receiving a checkpoint inhibitor in combination with a platinum-based doublet, as first-line treatment for NSCLC.
• •* Patients who have progressed on checkpoint inhibitor as second-line therapy, after receiving a platinum-based doublet as first-line therapy.
• •* Patients who have progressed on platinum-based doublet as second-line therapy, after receiving a checkpoint inhibitor as first-line therapy.
• •Patients must have disease progression on or after platinum-based chemotherapy for metastatic disease or within 6 months of completion of platinum-based chemotherapy administration as adjuvant/neoadjuvant chemotherapy or concurrent chemoradiation.
• •Absolute neutrophil count \>= 1,500/mcL.
• •Platelet count \>= 150,000/mcL.
• •Total bilirubin =\< 1 x institutional upper limit of normal (ULN). Patients with Gilbert's syndrome may enroll if direct bilirubin =\< 1.5 x institutional ULN.
• •Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) / alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3.0 x institutional ULN. Patients with metastatic liver disease may enroll if =\< 5 x ULN.
• •Glomerular filtration rate (GFR) \> 30 mL/min/1.73 m\^2.
• •Known human immunodeficiency virus (HIV) positive patients who meet the following criteria will be considered eligible:
• •* CD4 count \> 350 cells/mm\^3.
• •* Undetectable viral load within the last six months.
• •* HIV positive patients must be stable on highly active antiretroviral therapy (HAART). Clinically significant metabolic enzyme inducers are not permitted during this study (e.g., ritonavir, efavirenz, nevirapine).
• •* No history of acquired immune deficiency syndrome (AIDS)-defining opportunistic infections.
• •Eastern Cooperative Oncology Group (ECOG) performance status 0-1.
• •Life expectancy \>= 12 weeks.
• •The effects of MLN4924 (pevonedistat) on the developing human fetus are unknown. For this reason and because agents 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 participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study or within 4 months of completion, 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 4 months after completion of MLN4924 (pevonedistat) administration.
• •Female patients who:
• •Are postmenopausal for at least 1 year before the screening visit, or
• •Are surgically sterile, or If they are of childbearing potential,
• •Agree to practice 1 highly effective method and 1 additional effective (barrier) method of contraception, at the same time, from the time of signing the informed consent through 4 months after the last dose of study drug (female and male condoms should not be used together), or
• •Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[e.g., calendar, ovulation, symptothermal, postovulation methods\] withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception.) Male patients, even if surgically sterilized (i.e., status postvasectomy), who
• •Agree to practice effective barrier contraception during the entire study treatment period and through 4 months after the last dose of study drug (female and male condoms should not be used together), OR
• •Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[e.g., calendar, ovulation, symptothermal, postovulation methods for the female partner\] withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception.)
• •* 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 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.
• •* Left ventricular ejection fraction (LVEF) \>= 50% as assessed by echocardiogram or radionuclide angiography.
• •* Ability to understand and the willingness to sign a written informed consent document. Participants with impaired decision-making capacity (IDMC) who have a legally authorized representative (LAR) or caregiver and/or family member available will also be considered eligible.
• •* Patients with NSCLC harboring genomic aberrations (e.g. sensitizing EGFR, ALK, ROS1, NTRK, BRAF V600E mutation positive) must have received prior treatment with Food and Drug Administration (FDA) approved targeted therapy for patients for which FDA approved targeted therapies is available.