Inclusion Criteria:

          -  Patients must have histologically or cytologically confirmed stage IV non-small cell
             lung cancer, or recurrent non-small cell lung cancer which is not amenable to curative
             intent therapy.

          -  Documented disease progression on at least two prior lines of chemotherapy for
             advanced NSCLC. Progression within 6 months of adjuvant chemotherapy or definitive
             chemoradiation will count as one line of therapy.

          -  Age ≥18 years.

          -  ECOG performance status ≤2.

          -  Ability to take pills by mouth.

          -  Patients must have normal organ and marrow function as defined below:

          -  Leukocytes ≥3,000/mcL

          -  Absolute neutrophil count ≥1,500/mcL

          -  Platelets ≥100,000/mcL

          -  Hemoglobin ≥8.5 g/dL

          -  Total bilirubin ≤1.5 x institutional upper limit of normal (ULN)

          -  AST(SGOT)/ALT(SGPT) ≤2.5 × ULN or ≤5 x ULN if metastases to the liver

          -  Creatinine clearance ≥40 mL/min

          -  Patients with asymptomatic brain metastases are allowed, as long as they are stable
             and do not require treatment with anticonvulsants or escalating doses of steroids.
             Maximum daily dose of steroids should be prednisone 20 mg or equivalent. Radiation
             therapy for brain metastases must be completed at least 14 days prior to treatment on
             protocol.

          -  Women of child-bearing potential and men must agree to use highly effective
             contraception (if using hormonal birth control must add a second barrier method;
             abstinence) prior to study entry, for the duration of study participation as well as
             for at least 1 month after the last dose of IRX4204. Men treated or enrolled on this
             protocol must also agree to use highly effective contraception prior to the study, for
             the duration of study participation and 3 months after completion of IRX4204
             administration.

          -  Ability to understand and the willingness to sign a written informed consent document.

        Exclusion Criteria:

          -  Patients who have had chemotherapy or radiotherapy within 4 weeks prior to entering
             the study.

          -  Activating EGFR mutations detected in the tumor.

          -  Prior treatment with an EGFR tyrosine kinase inhibitor.

          -  Prior treatment with IRX4204 or another retinoid or rexinoid administered for the
             purpose of cancer treatment. Prior topical retinoid use is allowed.

          -  History of allergic reactions attributed to IRX4204 or erlotinib or to compounds of
             similar chemical or biologic composition.

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac
             arrhythmia, or psychiatric illness/social situations that would limit compliance with
             study requirements.

          -  Pregnant and nursing women.

          -  Patients with a history of another active malignancy within the past two years, with
             the exception of non-melanoma cutaneous malignancy, cervical carcinoma in situ, or
             ductal carcinoma in situ which has been successfully treated with curative intent
             therapy.

          -  Any gastrointestinal disorder expected to limit absorption of IRX4204 or erlotinib.

          -  Patients with a history of active thyroid disease. However, patients with a history of
             hypothyroidism maintained in euthyroid state by supplementation with thyroid hormone,
             or a thyroid hormone containing preparation may be enrolled.

          -  Patients taking coumarin-derived anticoagulants.