A Phase 2 Exploratory Study of Erlotinib and SNDX-275 in Participants With Non-small Cell Lung Carcinoma Who Are Progressing on Erlotinib

Inclusion Criteria: 1. Cytologically or histologically confirmed NSCLC of stage IIIb (pleural effusion) or IV 2. Disease is progressing (either no response to treatment or subsequent relapse after an objective response) on erlotinib treatment, based on at least 2 scans (the last being within 4 weeks of study enrollment and can serve as the baseline scan for the participant's screening into the study) 3. Recovered from any toxicity associated with the most recent cancer treatment (no greater than grade 1 toxicity on Common Terminology Criteria for Adverse Events scale or to prior baseline condition) 4. At least 1 measurable lesion ≥ 20 millimeters (mm) by conventional computed tomography (CT) scan or ≥ 10 mm by spiral CT scan 5. Eastern Cooperative Oncology Group performance score of 0, 1, or 2 and life expectancy of at least 3 months 6. Paraffin-embedded tumor specimen available for correlative studies 7. Male or female over 18 years of age 8. Hemoglobin ≥ 9.0 grams/deciliter; platelets ≥ 75 x 10\^9/liter (L); absolute neutrophil count ≥ 1.0 x 10\^9/L without the use of hematopoietic growth factors 9. Coagulation tests within the normal range 10. Bilirubin and creatinine less than 2 times the upper limit of normal for the institution 11. Aspartate aminotransferase and alanine aminotransferase less than 3 times the upper limit of normal for the institution 12. Potassium, magnesium and phosphorus within the normal range for the institution (supplementation is permissible) 13. Willing to use accepted and effective methods of contraception during the study (both men and women as appropriate) and for 3 months after the last dose of entinostat 14. Participant or legally acceptable representative has granted written informed consent before any study-specific procedure (including special screening tests) is performed Exclusion Criteria: 1. Prior stem cell transplant 2. Symptomatic central nervous system involvement 3. Prior treatment with an histone deacetylase inhibitor 4. Concurrent anticancer therapy, with the exception of radiotherapy for a non-target study lesion 5. Currently taking medication(s) on the prohibited medication list 6. Systemic chemotherapy or treatment with an investigational agent within 28 days before enrollment 7. Current use of valproic acid 8. Untreated or unstable brain metastases, or taken steroids for this condition within 4 weeks of study drug administration 9. Currently active second malignancy, or any malignancy within the last 5 years other than cured basal or squamous cell skin carcinoma, cervical carcinoma in situ, or superficial bladder cancer 10. Inability to swallow oral medications or a gastrointestinal malabsorption condition 11. Uncontrolled infection requiring intravenous antibiotics, antivirals, or antifungals, known human immunodeficiency virus infection, or active hepatitis B or C infection 12. Abnormal cardiac function as defined as clinically significant findings on electrocardiogram (multifocal premature ventricular complexes, ST-T wave changes consistent with myocardial infarction or acute ischemia, QTc greater than 500 milliseconds), tachycardia, or left ventricular ejection fraction less than 40% on multigated acquisition scan 13. Another serious or uncontrolled medical condition within 3 months of enrollment such as hypertension, diabetes mellitus, or suppressed immune system 14. Known hypersensitivity to benzamides 15. Morbid obesity 16. Women who are currently pregnant or breast-feeding 17. Participant is currently enrolled in (or completed within 28 days) another investigational drug study 18. Participant unavailable for on-study or follow-up assessments 19. Participant has any kind of medical, psychiatric, or behavioral disorder that places the participant at increased risk for study participation or compromises the ability of the participant to give written informed consent and/or to comply with study procedures and requirements