Carfilzomib in Combination With Sotorasib for the Treatment of Patients With KRAS G12C Mutated Advanced or Metastatic Non-small Cell Lung Cancer

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Age: ≥ 18 years * Eastern Cooperative Oncology Group (ECOG) ≤ 2 * Histologically confirmed NSCLC that is metastatic or advanced. The tumor must exhibit evidence of KRASG12C mutation which is determined by either a Clinical Laboratory Improvement Act (CLIA) certified ctDNA assay or by a CLIA certified tumor tissue assay * Measurable disease by RECIST v1.1 * Failed prior KRAS inhibitor * Fully recovered from the acute toxic effects (except alopecia) from prior anti-cancer therapy * Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better * Patients with new or progressive brain metastases (active brain metastases) or leptomeningeal disease are eligible if the treating physician determines that immediate central nervous system (CNS) specific treatment is not required and is unlikely to be required during the first cycle of therapy * Absolute neutrophil count (ANC) ≥ 1,500/mm\^3 (performed within 14 days prior to day 1 of protocol therapy) * NOTE: Growth factor is not permitted within 14 days of ANC assessment unless cytopenia is secondary to disease involvement * Hemoglobin (Hb) ≥ 9 g/dL (performed within 14 days prior to day 1 of protocol therapy) * Platelets ≥ 100,000/mm\^3 (performed within 14 days prior to day 1 of protocol therapy) * NOTE: Platelet transfusions are not permitted within 14 days of platelet assessment unless cytopenia is secondary to disease involvement * Total bilirubin ≤ 1.5 x upper limit of normal (ULN) (unless has Gilbert's disease) (performed within 14 days prior to day 1 of protocol therapy) * Aspartate aminotransferase (AST) ≤ 3 x ULN (or ≤ 5 x ULN in the setting of liver metastatic disease) (performed within 14 days prior to day 1 of protocol therapy) * Alanine aminotransferase (ALT) ≤ 5 x ULN (or ≤ 5 x ULN in the setting of liver metastatic disease) (performed within 14 days prior to day 1 of protocol therapy) * Creatinine clearance of ≤ 1.5 x ULN or glomerular filtration rate (GFR) ≥ 60 mL/min/1.73 m\^2 (performed within 14 days prior to day 1 of protocol therapy) * Women of childbearing potential (WOCBP): negative urine or serum pregnancy test (performed within 14 days prior to day 1 of protocol therapy) * If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Agreement by females and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 120 days after the last dose of protocol therapy. * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) Exclusion Criteria: * Chemotherapy or immunotherapy within 21 days prior to day 1 of protocol therapy * Radiation therapy within 14 days prior to day 1 of protocol therapy * KRAS inhibitor within 14 days prior to day 1 of protocol therapy * Investigational therapy within 28 days prior to day 1 of protocol therapy (or 5 half-lives, use whichever is shorter) * Inability to previously tolerate (240 mg, QD) sotorasib * History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agent * Clinically significant uncontrolled illness * Evidence of chronic hepatitis B virus (HBV) infection and HBV viral load detectable * Evidence of untreated chronic hepatitis C virus (HCV) infection. Patients with HCV infection currently on treatment are eligible if they have an undetectable HCV viral load * Active infection requiring antibiotics (not to be completed by day 1 of protocol therapy) * Known history of immunodeficiency virus (HIV) with detectable viral load * Prior or concurrent malignancy whose natural history or treatment has the potential to interfere with the safety or efficacy assessment of the investigational regimen * New York Heart Association (NYHA) class III or IV heart failure, myocardial infarction in the preceding 6 months, conduction abnormalities uncontrolled by medications * Females only: Pregnant or breastfeeding * Any other condition that would, in the investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)