RO4929097 and Erlotinib Hydrochloride in Treating Patients With Stage IV or Recurrent Non-small Cell Lung Cancer

Inclusion Criteria: * Dose-escalation portion: * Patients must have histologically or cytologically confirmed diagnosis of incurable NSCLC * Preference will be given to patients with NSCLC who have been treated with erlotinib, and have either responded initially and then experienced subsequent growth in one or more tumor deposits while continuing erlotinib (acquired resistance) or patients who have been treated with erlotinib and failed to demonstrate any response to it (intrinsic resistance) * Expansion cohort: patients must satisfy each of the following criteria: * Histologically or cytologically confirmed non-small cell lung cancer that is incurable (stage IV or recurrent) * Patients must not have received prior anti-EGFR therapy * Patients on both the dose escalation portion of the study and in the Expansion Cohort portion must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 10 mm with computed tomography (CT) scan with cuts at 2.5 or 5 mm * Patients on both portions of the study must have tumor amenable to core biopsy (or to incisional, excisional, or punch biopsy) for research purposes; the collaborating interventional radiologists will make the determination whether or not the patient has a tumor amenable to biopsy and whether or not the patient is medically an appropriate candidate for tumor biopsy * Any prior anticancer systemic therapy or radiotherapy must have been completed at least 4 weeks prior to initiation of therapy on this study; (Exception: patients may be entered within 2 weeks of radiotherapy if the radiotherapy was restricted to femur below the trochanter, humerus or more distal limb areas) * Dose escalation portion: * Unlimited prior therapy is permitted (including prior anti-EGFR therapy), with the exception that patients who have received prior therapy with a gamma-secretase inhibitor are not eligible * Prior therapy is not required * Preference will be given to NSCLC patients who have been treated with erlotinib with evidence of acquired or intrinsic resistance to erlotinib * Expansion cohort: * Patients may have received an unlimited number of prior systemic regimens for NSCLC (as adjuvant therapy, as therapy for locally advanced disease or as therapy for advanced disease) provided they have not received prior anti-EGFR therapy (small molecule or antibody, etc) or prior gamma-secretase inhibitors * Prior therapy is not required * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 60%) * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets\>= 100,000/mcL * Hemoglobin \>= 9 g/dL * Total bilirubin within normal institutional limits * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 X institutional upper limit of normal * Creatinine =\< 1.5 X institutional upper limit of normal * International normalized ratio (INR) =\< 1.7 X upper limit of normal (ULN) and the patient must not have received aspirin or Coumadin and the patient must not have received aspirin or Coumadin within the previous week or a therapeutic dose of a heparin product within the previous 24 hours * Women of childbearing potential must use two forms of contraception (i.e., barrier contraception and one other method of contraception) from at least 2 weeks prior to initiation of therapy on this study, for the duration of study participation, and for at least 2 months post-treatment; should a woman become pregnant or suspect she is pregnant while she or her partner are participating in this study and for 2 months after study participation, the patient should inform the treating physician immediately * Women of childbearing potential are required to have a negative serum pregnancy test (with a sensitivity of at least 25 mIU/mL) within 14 days prior to the first dose of RO4929097 and a negative serum or urine pregnancy test within 24 hours prior to the first dose of RO4929097; following initiation of therapy with RO4929097, a pregnancy test (serum or urine) will be administered every 3 weeks while on study; a positive urine test must be confirmed by a serum pregnancy test; prior to dispensing RO4929097, the investigator or designate must confirm and document the patient's use of two contraceptive methods, dates of negative pregnancy test, and confirm the patient's understanding of the teratogenic potential of RO4929097 * Patients with a positive pregnancy test who are unlikely to be pregnant may be considered for entry on this trial if they are deemed to be unlikely to be pregnant by an obstetrician or gynecologist and if the study sponsor is in agreement with their study entry * Female patients of childbearing potential are defined as patients who do not fall into either of the categories listed above and to whom any of the following apply: * Patients with regular menses * Patients, after menarche with amenorrhea, irregular cycles, or using a contraceptive method that precludes withdrawal bleeding * Women who have had tubal ligation * Female patients may be considered to NOT be of childbearing potential for the following reasons: * The patient has undergone total abdominal hysterectomy with bilateral salpingo-oophorectomy or bilateral oophorectomy * The patient is medically confirmed to be menopausal (no menstrual period) for 24 consecutive months * Men participating in the study must also use 2 methods of contraception including 1 barrier method * Breastfeeding should be discontinued if the mother is treated with RO4929097 * Patients with asymptomatic or minimally symptomatic brain metastases will not be required to undergo cranial radiation prior to being considered for this trial, and are eligible provided that it is not anticipated that they will require any of the following over the course of study treatment: * Corticosteroids for control of cerebral edema * Enzyme-inducing anticonvulsants * Radiotherapy, surgery, or other local therapy for the brain metastases * Able to swallow oral medications Exclusion Criteria: * Patients may not have received other systemic therapy or radiotherapy for their cancer within the previous 4 weeks prior to planned first day of therapy on this trial; (Exception: patients may be entered within 2 weeks of radiotherapy if the radiotherapy was restricted to distal limbs such as femur below the trochanter, humerus or more distal limb areas; in addition, patients in the dose escalation portion who have previously received erlotinib may start therapy on this trial as early as 1 week after stopping prior erlotinib provided all other study entry criteria are met) * Patients on the expansion cohort may not have received prior anti-EGFR therapy (small molecule tyrosine kinase inhibitor \[TKI\] or antibody); (Note: this in contrast to the dose escalation portion of the study in which patients with prior anti-EGFR therapy will be eligible) * Patients may not be receiving any other investigational agents * History of allergic reactions attributed to compounds of similar chemical or biologic composition to RO4929097, OSI-774 or other agents used in the study * Patients taking medications with narrow therapeutic indices that are metabolized by cytochrome P450 (CYP450), including warfarin sodium (Coumadin®) are ineligible * Caution should be exercised when dosing RO4929097 concurrently with CYP3A4 substrates, inducers, and/or inhibitors; furthermore, patients who are taking concurrent medications (other than erlotinib) that are strong inducers/inhibitors or substrates of CYP3A4 should be switched to alternative medications; if such patients cannot be switched to alternative medications, they will be ineligible to participate in this study; if a patient is taking a strong CYP3A4 inhibitor/inducer other than the 2 study drugs, they should be switched to an alternative drug * Patients with malabsorption syndrome or other condition that would interfere with intestinal absorption * Diarrhea \> grade 1 despite appropriate therapy * Patients who are known to be serologically positive for hepatitis A, B or C are ineligible * Patients with \> grade 1 (by Common Terminology Criteria for Adverse Events \[CTCAE\] criteria) hyponatremia or hypocalcemia (based on measurement of ionized calcium) despite appropriate medical management are excluded from this study, as are patients with hypophosphatemia (serum phosphate below the lower limit of normal for the institution), hypomagnesemia, (serum magnesium below the lower limit of normal), hypokalemia, or hyperkalemia (serum potassium outside normal limits) despite appropriate medical management * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection requiring systemic therapy (with antibiotics, antiviral or antifungal agents), symptomatic congestive heart failure, unstable angina pectoris, angina at rest, a history of torsades de pointes, potentially life-threatening cardiac arrhythmias (patients are permitted to have chronic, stable atrial fibrillation, premature atrial or ventricular contractions, sinus tachycardia, provided the rate is controlled at \< 115 per minute, and sinus bradycardia, provided the rate is \> 50 per minute), myocardial infarction within the previous 3 months, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible * Cardiovascular: baseline corrected QT interval using Fridericia's formula (QTcF) \> 450 msec (male) or QTcF \> 470 msec (female) * Patients requiring drugs that are known to cause Torsades de pointes and/or prolonged corrected QT (QTc) intervals are excluded; patients requiring drugs with a possible but unproven association with Torsades de pointes and/or QTc prolongation may be eligible, but will require additional electrocardiogram assessments, as outlined * Patients who have not recovered to \< CTCAE grade 2 toxicities related to prior therapy are not eligible to participate in this study