The purpose of this study is to test the safety of different ways of taking erlotinib. The investigators want to find out what effects, good and/or bad, combination daily low dose and twice weekly high dose erlotinib has on the patient and lung cancer. The investigators are also seeing whether different schedules of erlotinib are better at treating lung cancer that has spread to the central nervous system.

CNS expansion phase:

The pulse continuous regimen will be then assess in patients with EGFR mutant lung cancers and CNS involvement. An additional expansion cohort (A) will enroll 19 patients with newly diagnosed EGFR mutant lung cancer with CNS involvement at diagnosis. The patients in the expansion cohorts will undergo the same treatment plan as the patients in the dose expansion cohort. A patient in the expansion cohorts will not be replaced if he/she does not finish the first 28 day (cycle 1) treatment period.

Inclusion Criteria:

• MSKCC pathologically-proven diagnosis locally advanced Stage III not amenable to definitive, curative treatment or Stage IV or recurrent non-small cell lung cancer
• Documented presence of EGFR mutation confirmed by MSKCC or a local facility.
• No prior treatment with erlotinib, gefitinib, or other EGFR tyrosine kinase inhibitors
• Age ≥ 18 years
• Measurable (RECIST 1.1) indicator lesion not previously irradiated.
• Karnofsky Performance Status ≥ 70%
• Ability to take oral medications
• A negative serum pregnancy test obtained within 4 weeks prior to the start of treatment in all women of child-bearing potential.
• All women of child bearing potential and sexually active men must agree to use adequate methods of birth control throughout the study which includes use of oral contraceptives with an additional barrier methods, double barrier methods, Depo-Provera, permanent sterilization of patient or partner or total abstinence.

Expansion A:

• brain metastases or leptomeningeal not previously treated with radiation or surgery

Exclusion Criteria:

• Inadequate recovery from any toxicity related to prior treatment (to Grade 2 or baseline).
• Inadequate hematologic function defined as ANC < 1000 cells/mm³, Platelet count <75,000/mm³ or Hemoglobin <9.0g/dL.
• Inadequate hepatic function defined by AST/ALT >3x upper limit of normal (ULN), Total bilirubin>2x ULN, Alkaline phosphatase >3x ULN.
• Symptomatic brain metastasis requiring radiation therapy or escalating doses of steroids.
• Patients with clinically stable brain metastases or leptomeningeal disease (previously treated or untreated) are eligible. Patients in expansion cohort A must have at least one untreated CNS lesion
• Women who are breastfeeding or pregnant.
• Any evidence of clinically active interstitial lung disease.