Erlotinib Hydrochloride and Cabozantinib-s-Malate Alone or in Combination as Second or Third Line Therapy in Treating Patients With Stage IV Non-small Cell Lung Cancer

This randomized phase II trial studies how well giving erlotinib hydrochloride and cabozantinib-s-malate alone or in combination works as second or third line therapy in treating patient with stage IV non-small cell lung cancer. Erlotinib hydrochloride and cabozantinib-s-malate may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. It is not yet known whether giving erlotinib hydrochloride together with cabozantinib-s-malate is more effective than erlotinib hydrochloride or cabozantinib-s-malate alone in treating non-small cell lung cancer.

PRIMARY OBJECTIVES:

I. To compare the progression-free survival (PFS) associated with patients treated with erlotinib (erlotinib hydrochloride) versus (vs) erlotinib plus cabozantinib (cabozantinib-s-malate).

II. To compare the PFS associated with patients treated with erlotinib vs cabozantinib.

SECONDARY OBJECTIVES:

I. To evaluate overall survival in the three treatment arms. II. To evaluate best objective response rate in the three treatment arms. III. To define the toxicity associated with each regimen. IV. To conduct correlative science studies that will help to select predictive biomarkers of response to therapy, including mesenchymal-epidermal transition (MET) expression and potentially other tissue biomarkers, plasma biomarkers, and bone scans.

OUTLINE: Patients are randomized to 1 of 3 treatment arms.

ARM A (erlotinib): Patients receive erlotinib orally (PO) daily on days 1-28. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity.

ARM B (cabozantinib): Patients receive cabozantinib PO daily on days 1-28. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity.

ARM C (erlotinib+cabozantinib): Patients receive erlotinib as patients in Arm A and cabozantinib as patients in Arm B. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity.

ARM Z: Patients achieving disease progression in Arm A or Arm B may receive erlotinib and cabozantinib as patients in Arm C. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up every 3 months for 2 years and then every 6 months for 3 years.

Eligibility Criteria:
Criteria:

* Tumor with a sensitizing mutation in epidermal growth factor receptor (EGFR), defined as follows:

  * EGFR mutation testing of tumor has been performed and did not demonstrate an EGFR tyrosine kinase inhibitor sensitizing mutation; at minimum, testing for EGFR exon 19 deletion and exon 21 L858R mutations must have been included; OR
  * EGFR mutation testing has been attempted and is inconclusive (for example, due to lack of sufficient deoxyribonucleic acid \[DNA\] yield); OR
  * EGFR mutation status is unknown but tumor is positive for at least one alternative driver mutation, i.e: Kirsten rat sarcoma viral oncogene homolog (KRAS) mutation, v-raf murine sarcoma viral oncogene homolog B (BRAF) mutation, human epidermal growth factor receptor 2 (HER2) mutation, ret proto-oncogene (RET) rearrangement/fusion, or one not listed following approval by the study chair prior to registration

Inclusion Criteria:

* INCLUSION CRITERIA STEP 1:
* Cytologically or histologically confirmed non-small cell lung carcinoma (NSCLC)
* Predominant non-squamous histology (patients with NSCLC not otherwise specified \[NOS\] are eligible); mixed tumors will be categorized by the predominant cell type; if small cell elements are present the patient is ineligible
* Stage IV disease (includes M1a, M1b, or recurrent disease), according to the 7th edition of the lung cancer TNM classification system
* Patients must have measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) version (v) 1.1 criteria; baseline measurements and evaluation of all sites of disease must be obtained within 4 weeks prior to registration
* Prior to registration, the investigator/site must confirm that sufficient pathology material representative of patient's cancer is available for submission for MET immunohistochemical (IHC) testing
* Patients must have received one or two lines of prior chemotherapy (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
* Any prior chemotherapy (based on administration schedule) must have been completed in greater than or equal to the time frames specified in the protocol
* Patients must have discontinued treatment with any other type of investigational agent \>= 4 weeks prior to registration
* Patients must have recovered to baseline or Common Terminology Criteria for Adverse Events (CTCAE) v 4.0 =\< grade 1 from toxicity due to all prior therapies except alopecia and other non-clinically significant adverse events (AEs)
* Patients with no known brain metastasis at baseline must have baseline brain imaging within 12 weeks prior to study registration not demonstrating brain metastases; patients with brain metastases at baseline must have baseline brain imagining within 4 weeks prior to study registration and meet all of the specific criteria for brain mets listed in the protocol
* Radiation related toxicities must have resolved to =\< grade 1 prior to registration
* Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status between 0-2
* Patients must have an anticipated life expectancy greater than 3 months
* Acceptable bone marrow, renal and hepatic function within 2 weeks prior to registration as defined in the protocol
* Patients must have corrected QT interval calculated by the Fridericia formula (QTcF) =\< 500 ms within 28 days before registration
* Patients must be able to swallow tablets
* INCLUSION CRITERIA STEP 2:
* Patients must have met all eligibility requirements for Step 1 at time of registration to Step 1 to be eligible for Step 2
* Patients must have radiographic progressive disease per RECIST v1.1 criteria after \>= 2 courses of therapy on Arm A or Arm B
* Patients must be registered to Step 2 within 4 weeks of the last dose of treatment administration from Step 1
* Patients must have an ECOG performance status between 0-2
* Patients must have recovered to baseline (pre-Step 1) or CTCAE version 4.0 \<= grade 1 from toxicity due to all prior therapies except alopecia and other non-clinically significant AEs

Exclusion Criteria:

* EXCLUSION CRITERIA STEP 1:
* Patients without sufficient pathology material representative of the patient's cancer (tumor block or 10 unstained slides)
* Prior erlotinib, other EGFR tyrosine kinase inhibitor therapy, vascular endothelial growth factor receptor (VEGFR) tyrosine kinase inhibitor therapy, Met tyrosine kinase inhibitor therapy, or Met monoclonal antibody (MetMAb); prior antibody therapy such as bevacizumab or cetuximab is allowed with a washout period depending on dosing interval and investigational nature
* Prior radiation therapy to the thoracic cavity, abdomen, or pelvis within 3 months prior to registration, to bone or brain metastasis within 14 days prior to registration, or to any other site within 28 days prior to registration
* History of the following: Clinically-significant gastrointestinal (GI) bleeding within 6 months prior to registration; Hemoptysis of \>= 0.5 teaspoon (2.5 mL) of red blood within 3 months prior to registration; Any other signs indicative of pulmonary hemorrhage within 3 months prior to registration
* Radiographic or other evidence of the following within 28 days prior to registration: • Tumor invading the GI tract (esophagus, stomach, small or large bowel, rectum or anus), or any evidence of endotracheal or endobronchial tumor; Cavitating pulmonary lesion(s); Tumor in contact with, invading or encasing any major blood vessels
* Psychiatric illness/social situations that would limit compliance with study requirements
* History of major thrombotic events (deep vein thrombosis \[DVT\] or pulmonary embolism \[PE\]) within 6 months prior to registration
* Concomitant treatment, in therapeutic doses, with anticoagulants such as warfarin or warfarin-related agents, heparin, low molecular weight heparin (LMWH), thrombin or Factor Xa inhibitors, or antiplatelet agents (e.g., clopidogrel). (low dose aspirin \[=\< 81 mg/day\] and prophylactic LMWH are permitted)
* Concomitant treatment of strong cytochrome P450 3A4 (CYP3A4) inducers (e.g., dexamethasone, phenytoin, carbamazepine, rifampin, rifabutin, rifapentine, phenobarbital, and St. John's wort)
* Cardiovascular disorders including: Congestive heart failure (CHF): New York Heart Association (NYHA) class III (moderate) or class IV (severe) at the time of screening;
* Concurrent uncontrolled hypertension; Any history of congenital long QT syndrome; Any of the following within 6 months prior to registration:

  * Unstable angina pectoris
  * Clinically-significant cardiac arrhythmias
  * Stroke (including transient ischemic attack \[TIA\], or other ischemic event)
  * Myocardial infarction
* GI disorders particularly those associated with a high risk of perforation or fistula formation specified in the protocol
* Other disorders associated with a high risk of fistula formation including percutaneous endoscopic gastrostomy (PEG) tube placement within 3 months prior to registration
* Uncontrolled, significant, intercurrent or recent illness
* Prior malignancy within 2 years prior to registration which required systemic treatment or is currently active
* Pregnant or breast-feeding
* Patients with known human immunodeficiency virus (HIV) disease taking antiretroviral therapy
* Known chronic active hepatitis B
* EXCLUSION CRITERIA (STEP 2):
* Intervening anticancer treatment or major surgical procedure(s) between Step 1 and Step 2, except palliative radiation to the bone finishing \>= 2 weeks prior to registration to Step 2
* Central nervous system (CNS) progression; patients with stable CNS disease are allowed
* Intercurrent illness or disease complication that the investigator believes would limit the ability to safely tolerate the combination of erlotinib and cabozantinib