Pemetrexed Disodium and Carboplatin or Cisplatin With or Without Erlotinib Hydrochloride in Treating Patient With Stage IV Non-Small Cell Lung Cancer Resistant to First-Line Therapy With Erlotinib Hydrochloride or Gefitinib

Inclusion Criteria: * Signed informed consent prior to initiation of any study-specific procedure or treatment. Informed Consent Form must be signed within 14 days of study treatment initiation. * Age \> 18 years * Able and willing to comply with the protocol * Histologically- or cytologically-confirmed Stage IV NSCLC with an EGFR exon-19 deletion or L858R mutation * Must have received at least 6 months of first-line therapy with erlotinib or gefitinib * Clinical evidence of progression on first-line EGFR TKI therapy * Adequate hematological function within 7 days of study treatment initiation: 1. Absolute neutrophil count (ANC) \> 1.5 x 109/L AND 2. Platelet count \> 100 x 109/L AND 3. Hemoglobin \> 9 g/dL (may be transfused to maintain or exceed this level) * Adequate liver function within 7 days of study treatment initiation: 1. Total bilirubin \< 1.5 x upper limit of normal (ULN) AND 2. AST and ALT \< 2.5 x ULN in patients without liver metastases; \< 5 x ULN in patients with liver metastases * Adequate renal function within 7 days of study treatment initiation: a. Serum creatinine \< 1.25 x ULN or calculated creatinine clearance \> 50 mL/min (Creatinine clearance may be calculated per institutional standards.) * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 within 7 days of study treatment initiation * Patients with stable, treated brain metastases are eligible for study participation and may be on a stable dose of steroids at screening. Anticonvulsants (at stable dose) are allowed. Radiotherapy and stereotactic radiosurgery to the brain must be completed at least 28 days prior to randomization * Female patients must not be pregnant or breast-feeding. Female patients with childbearing potential should agree to use effective, non-hormonal means of contraception (intrauterine contraceptive device, barrier method of contraception in conjunction with spermicidal jelly or surgically sterile) during the study and for a period of at least 6 months following the last administration of study drugs. Female patients with an intact uterus (unless amenorrhoeic for the last 12 months) must have a negative serum pregnancy test within 7 days prior to randomization into the study. * Fertile male patients must agree to use effective contraception during the study and for a period of at least 3 months following the last administration of study drugs Exclusion Criteria: * Any other prior treatment for metastatic NSCLC other than erlotinib or gefitinib. Prior adjuvant chemotherapy or concurrent chemo-radiation therapy is allowed if completed at least 12 months prior to trial enrollment * Radiotherapy to the brain within 28 days prior to randomization, or radiotherapy to any other site up to 14 days prior to randomization * Clinically significant (i.e., active) cardiovascular disease (e.g., cerebrovascular accident or myocardial infarction within 6 months prior to randomization), unstable angina, congestive heart failure (New York Heart Association Class \> II), or serious cardiac arrhythmia, that is uncontrolled by medication or may interfere with administration of study treatment * Treatment with any other investigational agent or participation in another clinical trial that combines erlotinib with a second therapy unless the patient was on placebo. * Malignancies other than NSCLC within 3 years prior to randomization, except for adequately treated carcinoma in situ of the cervix, basal or squamous cell skin cancer, localized prostate cancer treated with radiation or surgically with curative intent, and ductal carcinoma in situ treated surgically with curative intent * Evidence of any other disease, neurological or metabolic dysfunction, physical examination finding or laboratory finding giving reasonable suspicion of a disease or condition that contraindicates the use of an investigational drug or puts the patient at high risk for treatment-related complications