ELIGIBILITY CRITERIA

          -  Age: Men and women aged >18 years,

          -  Signed written informed consent,

          -  Any histologic type of locally advanced or metastatic NSCLC,

          -  Life expectancy of ≥ 12 weeks,

          -  Measurable or evaluable (cytologically or radiologically detectable disease such as
             ascites, peritoneal deposits, or lesions which do not fulfill RECIST 1.1 criteria for
             measurable disease) lesions according to RECIST 1.1 criteria for phase 1 portion. For
             phase 2, all patients must have RECIST 1.1 measurable disease,

          -  Physiologic function:

               -  Hematologic: Absolute neutrophil count (ANC) ≥ 1.5 × 109/L, platelet count ≥ 100
                  × 109/L, and hemoglobin ≥ 9 g/dL (may have been transfused),

               -  Hepatic: Total bilirubin level ≤ 1.5 × the upper limit of normal (ULN) range and
                  aspartate aminotransferase (AST) and alanine aminotransferase (ALT) levels ≤ 2.5
                  × ULN,

               -  Renal: Estimated creatinine clearance ≥ 30 mL/min according to the
                  Cockcroft-Gault formula (or local institutional standard method).

          -  Pregnancy and contraception:

               -  Pregnancy test: Negative serum or urine pregnancy test at screening for women of
                  childbearing potential.

               -  Contraception: Highly effective contraception for both male and female subjects
                  throughout the study and for at least 90 days after last treatment administration
                  if the risk of conception exists.

          -  Ability to comply with protocol requirements,

          -  Willingness to consent and ability to undergo a trucut biopsy to obtain a fresh
             metastasis or primary tumor biopsy, and to undergo bronchoscopy to obtain a biopsy
             from normal bronchial mucosa,

          -  No serious or medically uncontrolled concomitant conditions that are likely to make
             the patient unfit for SPRING combination therapy, as per investigator assessment,

          -  ECOG performance status of 0 to 1.

        EXCLUSION CRITERIA

          -  Patients with documented oncogenic aberrations at enrollment: EGFR, ALK, ROS1 when
             available, MET exon 14 skipping when available. For squamous undifferentiated cell
             carcinoma, documentation of these aberrations is not mandatory. Note: For Phase 1
             portion, all patients with adenocarcinoma histology must have documentation of results
             for druggable oncogenic aberrations (EGFR mutations, ALK rearrangements, and ROS1 when
             available) prior to enrollment on the study.

          -  For Phase 1 portion, >2 lines of prior therapy in the metastatic setting.

          -  For the dose escalation phase of the study or until the MTD for the combination
             regimen has been determined, patients with moderate hepatic impairment defined as AST,
             ALT, alkaline phosphatase (ALP) >5 times ULN, which would be grade 3 or higher.
             However, patients with liver metastases with AST/ALT ≤ 5 x ULN can be included in the
             study.

          -  For Phase 2 portion, any prior therapy in the metastatic setting.

        Clinical criteria for phase 1 and phase 2 studies:

          -  Patients with treated brain metastases are eligible as are patients with new, active
             untreated brain metastasis.

          -  Participants with a history of myocardial infarction within the last 2 years or with
             significant cardiac arrhythmias uncontrolled by medication or pacemaker,

          -  Participants with any history of interstitial lung disease,

          -  Prior clinically significant toxicities from anticancer agents or radiotherapy which
             have not regressed to Grade ≤ 1 severity (NCI-CTCAE version 4.03) apart from
             peripheral neuropathy and alopecia,

          -  History of any second malignancy in the last two years; patients with prior history of
             in-situ cancer or basal or squamous cell skin cancer are eligible. Patients with a
             history of other malignancies are eligible if they have been continuously disease-free
             for at least two years,

          -  Autoimmune condition requiring medical intervention,

          -  Uncontrolled concomitant illness, active infection requiring i.v. antibiotics,

          -  Patients who have had a thromboembolic event within six months are excluded, as are
             patients on anticoagulants, except for low dose aspirin (<100 mg/day) and low doses of
             anticoagulants meant to keep line access open;

          -  Patients with Grade 3 or 4 (serious) gastrointestinal bleeding within the last six
             months are excluded.

          -  Prior > G3 hemoptysis, major blood vessel involvement (specifically including aorta,
             superior and inferior vena cave, main pulmonary arteries and veins, subclavian
             arteries and veins and other large blood vessels that in the investigator's opinion
             places the patients at high risk for major bleeding), and/or central cavitations,

          -  Known or suspected drug hypersensitivity to any drug used in the combination,

          -  Difficulty swallowing, malabsorption or other chronic gastrointestinal disease, or
             conditions that may hamper compliance and/or absorption of the oral drugs,

          -  Any condition (e.g., known or suspected poor compliance, psychological instability,
             geographical location, etc.) that, in the judgment of the investigator may affect the
             patient's ability to sign the informed consent and undergo study procedures,

          -  Taking another experimental drug within 28 days prior to day 1 of the protocol
             medications in this study,

          -  Pregnant or breast-feeding women,

          -  Both male and female patients of reproductive potential must agree to use highly
             effective contraception, during the study and for 3 months following the last dose of
             study drug,

          -  Patients currently taking strong CYP3A4 inducers and inhibitors,

          -  Patients currently taking proton pump inhibitors due to their impact on the
             disposition of palbociclib during the phase 1.

          -  Patients taking other anticancer agents with the exception of denosumab or equivalent
             medication for bone metastases.

          -  A time period of at least three weeks (including radiotherapy) or five drug
             half-lives, whichever is shorter must have elapsed from last non-investigational
             therapy before first day of treatment on this study,

          -  A time period of at least 10 days must have elapsed from last palliative radiotherapy
             before the first day of treatment on this study,

          -  Specific exclusion criteria for administration of avelumab, in combination:

               -  IMMUNOSUPRESSANTS: Current use of immunosuppressive medication, EXCEPT for the
                  following: a. intranasal, inhaled, topical steroids, or local steroid injection
                  (e.g., intra-articular injection); b. Systemic corticosteroids at physiologic
                  doses ≤ 10 mg/day of prednisone or equivalent; c. Steroids as premedication for
                  hypersensitivity reactions (e.g., CT scan premedication).

               -  AUTOIMMUNE DISEASE: Active autoimmune disease that might deteriorate when
                  receiving an immuno-stimulatory agent. Patients with diabetes type I, vitiligo,
                  psoriasis, or hypo- or hyperthyroid diseases not requiring immunosuppressive
                  treatment are eligible.

               -  ORGAN TRANSPLANTATION: Prior organ transplantation including allogenic stem-cell
                  transplantation.

               -  INFECTIONS: Active infection requiring IV (Intra venous) therapy.

               -  HIV/AIDS: Known history of testing positive for HIV or known acquired
                  immunodeficiency syndrome.

               -  HEPATITIS: Hepatitis B virus (HBV) or hepatitis C virus (HCV) infection at
                  screening (positive HBV surface antigen or HCV RNA if anti-HCV antibody screening
                  test positive).

               -  VACCINATION: Vaccination within 4 weeks of the first dose of avelumab and while
                  on trials is prohibited except for administration of inactivated vaccines.

               -  HYPERSENSITIVITY TO STUDY DRUG: Known prior severe hypersensitivity to
                  investigational product or any component in its formulations, including known
                  severe hypersensitivity reactions to monoclonal antibodies (NCI CTCAE v4.03 Grade
                  ≥ 3).

               -  CARDIOVASCULAR DISEASE: Clinically significant (i.e., active) cardiovascular
                  disease: cerebral vascular accident/stroke (< 6 months prior to enrollment),
                  myocardial infarction (< 6 months prior to enrollment), unstable angina,
                  congestive heart failure (≥ New York Heart Association Classification Class II),
                  or serious cardiac arrhythmia inadequately controlled by medication.

               -  OTHER PERSISTING TOXICITIES: Persisting toxicity related to prior therapy (NCI
                  CTCAE v. 4.03 Grade > 1); however, alopecia, sensory neuropathy Grade ≤ 2, or
                  other Grade ≤ 2 not constituting a safety risk based on investigator's judgment
                  are acceptable.

               -  Other severe acute or chronic medical conditions including colitis, inflammatory
                  bowel disease, pneumonitis, pulmonary fibrosis or psychiatric conditions
                  including recent (within the past year) or active suicidal ideation or behavior;
                  or laboratory abnormalities that may increase the risk associated with study
                  participation or study treatment administration or may interfere with the
                  interpretation of study results and, in the judgment of the investigator, would
                  make the patient inappropriate for entry into this study.