Phase 1 Erlotinib and Dovitinib (TKI258) in Advanced Non-small Cell Lung Cancer (NSCLC)

Inclusion Criteria: * Histologically-confirmed metastatic non-small cell lung cancer * One or more primary or metastatic lesions measurable in at least one dimension by modified Response Evaluation Criteria In Solid Tumors (RECIST) criteria (v1.1) within 4 weeks prior to entry of study * Patients who have failed any number of prior therapies, including those previously treated with erlotinib * Life expectancy \> 2 months * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L (\>= 1500/mm\^3) * Platelets (PLT) \>= 100,000/mm\^3 * Hemoglobin (Hgb) \>= 9 g/dL * Serum creatinine =\< 1.5 x upper limit of normal (ULN) * Serum bilirubin =\< 1.5 x ULN (regardless of whether liver metastases are present at baseline) * Aspartate aminotransferase (AST)/serum glutamic oxaloacetic transaminase (SGOT) and alanine aminotransferase (ALT)/serum glutamic pyruvic transaminase (SGPT) =\< 3.0 x ULN (regardless of whether liver metastases are present at baseline) * Ability to understand and the willingness to provide verbal and written informed consent * Patients - both males and females- with reproductive potential (i.e. menopausal for less than 1 year and not surgically sterilized) must practice effective contraceptive measures throughout the study; women of childbearing potential must provide a negative pregnancy test (serum or urine) within 14 days prior to registration Exclusion Criteria: * Patients who have received the last administration of chemotherapy or immunotherapy =\< the timeframe defined below after the end of the cycle of the last treatment, prior to starting study drug, or who have not recovered from the side effects of such therapy: * Patients who have received the last administration of chemotherapy/immunotherapy in a daily schedule =\< 7 days prior to starting study drug * Patients who have received the last administration of chemotherapy/immunotherapy in a weekly schedule =\< 2 weeks prior to starting study drug * Patients who have received the last administration of chemotherapy/immunotherapy in a 2-weekly schedule =\< 3 weeks prior to starting study drug * Patients who have received the last administration of chemotherapy/immunotherapy in a 3-weekly schedule =\< 4 weeks prior to starting study drug * Patients who have received the last administration of chemotherapy/immunotherapy in a 4-weekly schedule =\< 5 weeks prior to starting study drug * Patients who have received the last administration of nitrosourea, mitomycin-C =\< 6 weeks prior to starting study drug, or who have not recovered from the side effects of such therapy * Patients who have received wide field radiotherapy (including therapeutic radioisotopes such as strontium 89) =\< 4 weeks or limited field radiation for palliation =\< 2 weeks prior to starting study drug or who have not recovered from side effects of such therapy * Patients who have undergone major surgery =\< 4 weeks prior to starting study drug or who have not recovered from side effects of such therapy * If history of other primary cancer, subject will be eligible only if she or he has: * Curatively resected non-melanomatous skin cancer, basal cell carcinoma, squamous cell carcinoma * Curatively treated cervical carcinoma in situ * Other primary solid tumor curatively treated with no known active disease present and no treatment administered for the last 3 years * Subjects known to have chronic or active hepatitis B or C infection with impaired hepatic function (ineligible if AST and ALT \> 2.5 x ULN) * History of any medical or psychiatric condition or laboratory abnormality that in the opinion of the investigator may increase the risks associated with study participation or study drug administration or may interfere with the conduct of the study or interpretation of study results * Patients who continue to smoke (given that smoking decreases serum levels of erlotinib) * Female subject who is breast-feeding or who has positive serum pregnancy test 72 hours prior to enrollment * Any of the following concurrent severe and/or uncontrolled medical conditions within 6 months of enrollment which could compromise participation in the study: * Unstable angina pectoris * Uncontrolled hypertension defined by a systolic blood pressure (SBP) \>= 160 mm Hg and/or diastolic blood pressure (DBP) \>= 100 mm Hg, with or without anti-hypertensive medication; initiation or adjustment of antihypertensive medication(s) is allowed prior to study entry * Left ventricular ejection fraction (LVEF) assessed by 2-D echocardiogram (ECHO) \< 50% or lower limit of normal (whichever is higher) or multiple gated acquisition scan (MUGA) \< 45% or lower limit of normal (whichever is higher) * Myocardial infarction * Serious uncontrolled ventricular arrhythmia * Clinically significant resting bradycardia * Uncontrolled diabetes * Transient Ischemic Attach (TIA) * Cerebrovascular accident (CVA) * Pulmonary embolism (PE) * Impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of dovitinib (e.g. ulcerative diseases, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or small bowel resection) * Serious active or uncontrolled infection * Interstitial pneumonia or extensive and symptomatic interstitial fibrosis of the lung * Chronic renal disease * Cirrhosis, chronic active hepatitis or chronic persistent hepatitis * Patients who are currently receiving anticoagulation treatment with therapeutic doses of warfarin or enoxaparin * Women of child-bearing potential, who are biologically able to conceive, not employing two forms of highly effective contraception; highly effective contraception (e.g. male condom with spermicide, diaphragm with spermicide, intra-uterine device) must be used by both sexes during the study and must be continued for 8 weeks after the end of study treatment; oral, implantable, or injectable contraceptives may be affected by cytochrome P450 interactions, and are therefore not considered effective for this study; women of child-bearing potential, defined as sexually mature women who have not undergone a hysterectomy or who have not been naturally postmenopausal for at least 12 consecutive months (e.g., who has had menses any time in the preceding 12 consecutive months), must have a negative serum pregnancy test =\< 14 days prior to starting study treatment * Patients unwilling to or unable to comply with the protocol * There may be danger of harm to study participants because of human immunodeficiency virus (HIV) comorbidity or drug interactions