This randomized phase II trial studies how well pemetrexed disodium with or without erlotinib hydrochloride works in treating patients with stage IIIB-IV or recurrent non-small cell lung cancer. Drugs used in chemotherapy, such as pemetrexed disodium, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Erlotinib hydrochloride may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. It is not yet known whether pemetrexed disodium is more effective with or without erlotinib hydrochloride in treating non-small cell lung cancer.

PRIMARY OBJECTIVES:

I. To evaluate progression free survival (PFS) in the schedule-modulated concomitant administration of erlotinib (erlotinib hydrochloride) and pemetrexed (pemetrexed disodium), and in single agent pemetrexed in patients with advanced non-small cell lung cancer (NSCLC) as second-line chemotherapy.

SECONDARY OBJECTIVES:

I. To evaluate antitumor objective response rate (complete response [CR] + partial response [PR]) per Response Evaluation Criteria in Solid Tumors (RECIST) criteria.

II. To evaluate disease control rate (response rate + stable disease, i.e., CR+PR+ stable disease [SD]) and duration of response.

III. To evaluate median time to progression (TTP) and overall survival (OS). IV. To evaluate the safety profile of concurrent pemetrexed and erlotinib versus single agent pemetrexed.

TERTIARY OBJECTIVES:

i. To determine several molecular and cellular biomarkers in the tumors, the skin and the serum that are predictive of the efficacy of pemetrexed and erlotinib.

OUTLINE: Patients are randomized to 1 of 2 treatment arms.

ARM A: Patients receive pemetrexed disodium intravenously (IV) over 10 minutes on day 1. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity.

ARM B: Patients receive pemetrexed disodium IV as in Arm A and erlotinib hydrochloride orally (PO) once daily (QD) on days 2-17. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up for 12 months.

Inclusion Criteria:

• Patients must have histologically or cytologically confirmed advanced (stage IIIB with a malignant pleural effusion or stage IV disease) or recurrent nonsquamous NSCLC
• Patients must have at least one measurable disease per RECIST criteria; all sites of disease must be assessed within 4 weeks prior to registration
• Patient must have disease progression after one prior combinational chemotherapy and/or targeted therapy other than pemetrexed or an epidermal growth factor receptor (EGFR) ) tyrosine kinase inhibitor (TKI) (such as erlotinib, gefitinib, or a second generation EGFR TKI); prior monoclonal antibody against EGFR is allowed) for metastatic disease, or relapse while receiving adjuvant therapy, or within 12 months of completing adjuvant therapy
• All patients will be screened for brain metastasis within 6 weeks prior to registration; patients with treated and stable brain metastases must have been treated with surgery and/or radiation and are asymptomatic and are no longer taking corticosteroids
• Eastern Cooperative Oncology Group (ECOG) performance status =< 2 or Karnofsky >= 60%
• Absolute neutrophil count >= 1,500/uL
• Hemoglobin >= 8.0 g/dL
• Platelets >= 100,000/uL
• Total bilirubin =< 1.5 x institutional upper limit of normal (ULN), except in known hepatic metastasis, wherein may be =< 3.0 X ULN
• Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 3.0 x institutional ULN, except in known hepatic metastasis, wherein may be =< 5.0 X ULN
• Creatinine clearance >= 45 mL/min for patients with creatinine levels above institutional normal
• Patients must not be pregnant or breastfeeding since there is no information regarding the use of these agents in this population; a negative serum or urine pregnancy test is required within 14 days prior to registration if pre- or perimenopausal (i.e., last menstrual period within one year of registration); both pemetrexed and erlotinib are Class D agent with the potential for teratogenic or abortifacient effects; patients both females and males with reproductive potential (i.e. menopausal for less than 1 year and not surgically sterilized) must practice contraceptive measures throughout the study
• Patients taking Warfarin or nonsteroidal anti-inflammatory drugs (NSAIDs) are eligible; patients with mild to moderate renal insufficiency should avoid taking NSAIDs with short elimination half-lives for a period of 2 days before, the day of, and 2 days following administration of Alimta; if the patient is taking other cytochrome P450 3A4 (CYP3A4) inducers or inhibitors, they must be discontinued at least one week prior to starting erlotinib
• Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

• Patients who have had immunotherapy, hormone, chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier
• Patients who have received pemetrexed or an EGFR TKI (such as erlotinib, gefitinib, or a second generation anti-EGFR TKI) for their metastatic disease should be excluded from this clinical trial; other molecularly targeted agent, including monoclonal antibody or vaccine against EGFR or angiogenesis inhibitor, is allowed
• Patients may not be receiving any other investigational or commercial agents or therapies other than those described below with the intent to treat the patient's malignancy
• Patients with uncontrolled brain metastases should be excluded from this clinical trial because of their poor prognosis
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to erlotinib or pemetrexed or other agents used in the study
• Patients with gastrointestinal tract disease resulting in an inability to take oral medication or a requirement for IV alimentation, prior surgical procedures affecting absorption, or active peptic ulcer disease, are ineligible
• Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection (such as bacteremia or active hepatitis), symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
• Patients with immune deficiency are at increased risk of lethal infections when treated with marrow-suppressive therapy; therefore, human immunodeficiency virus (HIV)-positive patients receiving combination anti-retroviral therapy are excluded from the study because of possible pharmacokinetic interactions with erlotinib or pemetrexed or other agents administered during the study; appropriate studies will be undertake in patients receiving combination anti-retroviral therapy when indicated