Erlotinib Hydrochloride in Treating Non-Small Cell Lung Cancer That is Metastatic or Cannot be Removed by Surgery in Patients With HIV Infection

Inclusion Criteria: * Participants must have known HIV infection and histologically confirmed non-small cell lung cancer that is metastatic or unresectable; patients will be eligible regardless of tumor EGFR mutation status * Participants may have received any number of prior lines of chemotherapy (other than erlotinib or other EGFR-targeted therapy) for incurable non-small cell lung cancer; (first line platinum-doublet based chemotherapy plus switch maintenance chemotherapy counts as one line of therapy; prior adjuvant chemotherapy for early stage disease does not count as one line of therapy if 12 months or greater elapsed between completion of adjuvant therapy and initiation of first-line systemic therapy; if less than 12 months elapsed, adjuvant chemotherapy counts as one line of therapy) * PARTICIPANTS WITH NO PRIOR THERAPY FOR INCURABLE LUNG CANCER: trial eligibility will be restricted to those participants whose tumors harbor known EGFR activating mutations * PARTICIPANTS WITH PRIOR LINES OF THERAPY: all other participants (those whose tumors harbor wild-type EGFR or unknown EGFR status, or those with EGFR mutations not previously treated with erlotinib/EGFR-targeted therapy) * At least 4 weeks must have elapsed since prior chemotherapy or biological therapy, 6 weeks if the regimen included carmustine (BCNU) or mitomycin C; prior radiation therapy to the thoracic cavity, abdomen, or pelvis must be completed at least 3 months prior to registration; radiotherapy to any other site (including bone or brain metastases) must be completed at least 28 days prior to registration * Molecular characterization of non-squamous non-small cell lung cancer will be recommended prior to enrollment per standard of care/institutional guidelines; consistent with current National Comprehensive Cancer Network (NCCN) guidelines and the recent Food and Drug Administration (FDA)-approval indication of erlotinib for first-line treatment of advanced non-small cell lung cancer in persons with tumor EGFR mutations, participants who have known EGFR sensitizing mutations in tumors will be permitted to enter the study and receive erlotinib as initial monotherapy; for participants who have received one or more prior lines of chemotherapy, molecular characterization of tumors is required whenever possible with an understanding that inability to obtain sufficient tissue specimen for characterization will not preclude enrollment into the study * Participants must have measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1 criteria; baseline measurements and evaluation of ALL sites of disease must be obtained within 4 weeks prior to registration * Serologic documentation of HIV infection at any time prior to study entry, as evidenced by positive enzyme-linked immunosorbent assay (ELISA), positive Western blot, or any other federally approved licensed HIV test; alternatively, this documentation may include a record that another physician has documented that the participant has HIV infection based on prior ELISA and Western blot, or other approved diagnostic tests * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Life expectancy of greater than 12 weeks * Leukocytes: \>= 3,000/mm\^3 * Absolute neutrophil count: \>= 1,500/mm\^3 * Platelets: \>= 100,000/mm\^3 * Total bilirubin: within normal institutional limits; if, however, the participant has Gilbert's disease or unconjugated hyperbilirubinemia which is felt to be secondary to with atazanavir or indinavir therapy, then the total bilirubin must be =\< 3 x upper limit of normal \[ULN\]) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) / alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]): =\<2.5 x institutional upper limit of normal * Hemoglobin: \>= 9 g/dL * Creatinine: * Creatinine levels within normal institutional limits (\< 1.5 x ULN); or, * Creatinine clearance \>= 60 mL/min/1.73 m\^2 for participants with creatinine levels above institutional normal * A cluster of differentiation (CD)4+ lymphocyte count \> 50/mcL will be required within 2 weeks of study participation * Women of childbearing potential must have a negative pregnancy test within 7 days of enrollment; women of childbearing potential include women who have experienced menarche and who have not undergone successful surgical sterilization (hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or are not postmenopausal; postmenopause is defined as amenorrhea \>= 12 consecutive months; note: women who have been amenorrheic for 12 or more months are still considered to be of childbearing potential if the amenorrhea is possibly due to prior chemotherapy, anti-estrogens, ovarian suppression, or any other reversible reason * 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, 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 erlotinib administration * Participants MUST receive appropriate care and treatment for HIV infection, including antiretroviral medications, when clinically indicated and should be under the care of a physician experienced in HIV management; participants will be eligible regardless of antiretroviral medication (including no antiretroviral medication) provided there is no intention to initiate therapy or the regimen has been stable for at least 4 weeks with no intention to change the regimen within 8 weeks following study entry; as study-specific (antiretroviral-based) strata fill, however, only participants who are receiving the therapies eligible for the remaining open strata will be accrued * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Participants who received prior treatment with erlotinib or other EGFR-targeted agents * Participants who have had chemotherapy or radiotherapy within 4 weeks prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Participants who are receiving any other investigational agents * The participant has active brain metastases or epidural disease; participants with stable brain metastases previously treated with whole brain radiation or radiosurgery or participants with epidural disease previously treated with radiation or surgery who are asymptomatic and do not require steroid treatment for at least 4 weeks before starting study treatment are eligible; neurosurgical resection of brain metastases or brain biopsy is permitted if completed at least 3 months before starting study treatment; baseline brain imaging with contrast-enhanced computed tomography (CT) or magnetic resonance imaging (MRI) scans for participants with known brain metastases is required to confirm eligibility * History of allergic reactions attributed to compounds of similar chemical or biologic composition to erlotinib * The participant has prothrombin time (PT)/international normalized ratio (INR) or partial thromboplastin time (PTT) test \>= 1.3 the laboratory ULN within 7 days before the first dose of study treatment * 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 * Participants with history of chronic diarrhea, grade \>= 2 prior to study participation; persons with up to grade 1 diarrhea will be eligible * The participant requires chronic concomitant treatment with the following strong cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) inducers OTHER than antiretroviral agents: dexamethasone, phenytoin, carbamazepine, rifampin, rifabutin, rifapentine, phenobarbital, primidone, modafinil, and other enzyme inducing anti-convulsant drugs (EIACD), and St. John's Wort; use of efavirenz or etravirine is permitted for participants considered for the CYP3A4-inducer based antiretroviral therapy (ART) regimen arm (Stratum B) of the trial * Although study participants will be eligible regardless of smoking history, smokers should be strongly advised to stop smoking while on erlotinib; smoking induces cytochrome P450, family 1, subfamily A, polypeptide 2 (CYP1A2) enzymes and alters erlotinib exposure by 64% * Participants who take medications that are not recommended for concomitant use with their current antiretroviral regimen * The participant requires concomitant treatment with the following inhibitors of CYP3A4: * Antibiotics: clarithromycin, erythromycin, telithromycin, troleandomycin * Antifungals: itraconazole, ketoconazole, voriconazole, fluconazole, posaconazole * Antidepressants: nefazodone * Antidiuretic: conivaptan * Gastrointestinal (GI): cimetidine, aprepitant * Hepatitis C: boceprevir, telaprevir * Miscellaneous: Seville oranges, grapefruit, or grapefruit juice and/or pummelos, star fruit, exotic citrus fruits, or grapefruit hybrids); use of any of anti-retrovirals (delavirdine) or protease inhibitors (ritonavir, indinavir, lopinavir/ritonavir, saquinavir, nelfinavir) is permitted; specifically, ritonavir and cobicistat is permitted for participants considered for the CYP3A4-inhibitor based ART regimen arm (Stratum A) of the trial * Participants should not have significant abnormalities of the cornea based on history (e.g., dry eye syndrome, Sjogren's syndrome), congenital abnormality (e.g., Fuch's dystrophy), abnormal slit-lamp examination using a vital dye (e.g., fluorescein, Bengal-Rose), and/or an abnormal corneal sensitivity test (Schirmer test or similar tear production test) * Female participants may not be pregnant or breastfeeding; women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control) 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 should inform her treating physician immediately * Persons with tumors known to have biomarkers predictive of resistance to erlotinib therapy (specifically Kirsten rat sarcoma viral oncogene homolog \[KRAS\] mutations, anaplastic lymphoma receptor tyrosine kinase \[ALK\] gene rearrangements, and EGFR T790M mutations) will be ineligible for study participation; if the results of molecular studies are not available or known at the time of study registration and subsequently become available, such participants will be considered eligible and if deriving clinical benefit may continue receiving erlotinib at the discretion of the investigator and study chair