Neuroprotective Effects of Lithium in Patients With Small Cell Lung Cancer Undergoing Radiation Therapy to the Brain

Inclusion Criteria: * Patient must have histologically or cytologically confirmed small cell lung cancer. Patients with either limited or extensive stage disease are eligible. * Patient must have completed 4-6 cycles of platinum-based chemotherapy (+/- thoracic radiotherapy). * Patient must have no evidence of progressive disease on restaging imaging within 3 months of enrollment * For patients taking medications known to have a significant interaction with lithium carbonate, these medications should be discontinued at least 1 week prior to and during lithium treatment * Patient must be \> or = 18 years old. * Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2 * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin =\< 1.5 x institutional upper limit of normal (IULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvate transaminase \[SGPT\]) =\< 3.0 x IULN * Creatinine within normal institutional limits OR creatinine clearance \>= 50 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Patient must have an electrocardiogram without evidence of arrhythmia, QT prolongation (QTc \> 450 ms in males and \> 470 ms in females), or other severe dysfunction within 2 weeks of initiation of lithium * Women of childbearing potential (women with regular menses, women with amenorrhea, women with irregular cycles, women using a contraceptive method that precludes withdrawal bleeding, and women who have had a tubal ligation) are required to have a negative urine pregnancy test within 14 days prior to the first dose of lithium. * Women of childbearing 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 participating in this study, she must inform her treating physician immediately * Patient (or legally authorized representative if applicable) must be able to understand and willing to sign an Internal Review Board (IRB) approved written informed consent document Exclusion Criteria: * Patient must not have history of prior cranial radiotherapy * Patient must not have brain metastases present prior to initiation of initial therapy or PCI * Patient must not have evidence of progressive disease * Patient must not have received chemotherapy within 3 weeks of initiation of PCI * Patient must not have a history of other malignancy =\< 2 years previous with the exception of basal cell or squamous cell carcinoma of the skin which were treated with local resection only or carcinoma in situ of the cervix * Patient must not be actively receiving any other investigational agents * Patient must not have a history of allergic reactions attributed to compounds of similar chemical or biologic composition to lithium carbonate * Patient must not have any uncontrolled intercurrent illness including, but not limited to, ongoing or active infection symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Patient must not have any uncontrolled thyroid disease * Patient must not have a seizure disorder * Patient must not be pregnant and/or breastfeeding