Lung-MAP: Palbociclib as Second-Line Therapy in Treating Cell Cycle Gene Alteration Positive Patients With Recurrent Stage IV Squamous Cell Lung Cancer

Inclusion Criteria: * Patients must meet all SCREENING/PRE-SCREENING and SUB-STUDY REGISTRATION COMMON ELIGIBILITY CRITERIA as specified in S1400: Phase II/III Biomarker-Driven Master Protocol for Previously Treated Squamous Cell Lung Cancer (Lung-Map) * Patients must be assigned to S1400C * Patients must not be taking within 7 days prior to sub-study registration, nor plan to take while on protocol treatment and for 14 days after the last dose of study treatment, strong CYP3A4 inhibitors and/or strong CYP3A4 inducers; moderate inhibitors or inducers of isoenzyme CYP3A4 should be avoided, but if necessary can be used with caution * Patients must not be taking within 7 days prior to sub-study registration, nor plan to take while on protocol treatment drugs that are known to prolong the QT interval * Patients must not have a screening corrected QT Fridericia?s formula (QTcF) interval \> 480 msec based on the average of the triplicate electrocardiograms (EKGs) performed within 28 days prior to registration; NOTE: triplicate EKGs are required at other timepoints; patients must not have any family or personal history of long or short QT syndrome, Brugada syndrome or known history of QTc prolongation, or torsade de pointes * Patients must be able to take oral medications; patient may not have any impairment of gastrointestinal function or gastrointestinal disease that may significantly alter the absorption of palbociclib (e.g. ulcerative disease, uncontrolled nausea, vomiting, dia…