Deciphering Antitumour Response and Resistance With INtratumour Heterogeneity

Inclusion Criteria: TRACERx Patients * Multi-region sequencing data of the primary tumour available. * TRACERx patients should be approached for a biopsy of the active locally advanced or metastatic disease but this is not mandated for DARWIN2 trial inclusion. Consent for this biopsy will be obtained within the TRACERx study. Non-TRACERx patients Minimum requirement: • Fresh frozen biopsy of active locally advanced or metastatic disease OR at least two FFPE regions from primary tumour available Optimal Tissue availability: * Multi-region tissue of the primary tumour available (FFPE or fresh frozen) AND a fresh frozen biopsy of active locally advanced or metastatic disease * OR One archival biopsy tissue sample (FFPE or fresh frozen)/pre-extracted DNA sample AND one fresh frozen biopsy of active locally advanced or metastatic disease * OR Two fresh biopsies of active locally advanced or metastatic disease that are spatially separated e.g. one lymph node biopsy AND one lung biopsy. Consent for the biopsy(ies) of the active locally advanced or metastatic disease for non-TRACERx patients must be taken using the DARWIN2 'trial entry tissue sample' consent form. * Arm 1: Absence of any actionable mutation * ECOG PS 0-1 for MPDL3280A in combination with chemotherapy * ECOG PS 0-2 for MPDL3280A monotherapy. * Ability to avoid ibuprofen 2 days before, the day of, and 2 days following administration of Pemetrexed (combination therapy involving pemetrexed only) * Ability to take folic acid, Vitamin B12, and dexamethasone according to protocol (combination therapy involving pemetrexed only): * Arm 2: Presence of BRAFV600 mutation \- ECOG PS 0-2 for arm 2 * Arm 3: Presence of ALK/RET gene fusion and ALK IHC+/RET FISH \- ECOG PS 0-2 for arm 3 * Arm 4: Presence of HER2 amplification and HER2 IHC 3+ only \- ECOG PS 0-1 for arm 4. * Absence of sensitising EGFR mutation (tested according to local protocol). The only exception will be patients who progress on DARWIN1 or on EGFR TKi off-study e.g. standard of care (if agreed following prior discussion with the CI \& UCL CTC), or patients with squamous cell carcinoma * Absence of ALK fusions (tested according to local protocol) except for patient being considered for arm 3. Patients with squamous cell carcinoma do not require local testing for EGFR sensitising mutations and ALK fusions prior to inclusion for the trial. * Written Informed consent for DARWIN2. * Measurable disease by RECIST v1.1. Patients without measurable disease may be eligible following discussion with the CI and UCL CTC but will not count towards the PFS primary endpoint. See Appendix 4. * At least 18 years of age. * Anticipated life expectancy of at least three months. * Able to swallow and retain oral medication for arms 2 \& 3. * Adequate organ function as defined by the following baseline values: * Absolute neutrophil count (ANC) ≥1.5x109/L * Platelets ≥100x109/L * Serum bilirubin ≤1.5 x upper limit of normal (ULN). (In case of Gilberts syndrome discuss with TMG) * Aspartate aminotransferase (AST) or Alanine aminotransferase (ALT) ≤3xULN or ≤5x ULN if liver metastases are present). \* * Creatinine clearance must be \>30mL/min calculated or measured. * Women with child-bearing potential, or men who are able to father a child, must be willing to practice highly effective methods of birth control during the trial and for 7 months after the end of treatment. * Women of childbearing potential must have a negative pregnancy test within 14 days before registration. Exclusion Criteria: * Suitable for radical radiotherapy. * Palliative radiotherapy within 1 week prior to registration. * Patients with current or pre-existing interstitial lung disease. * Patients with active pre-existing autoimmune disease (some exceptions allowed). * Known hypersensitivity to study IMP or to any of the excipients * Inability to understand or to comply with the requirements of the trial, trial protocol or to provide informed consent. * Anti-cancer therapy including chemotherapy, radiation therapy (palliative dose within 7 days), immunotherapy (other than MPDL3280A (Atezolizumab) for Arm 1), biologic therapy, or major surgery within 14 days prior registration. * Known human immunodeficiency virus (HIV), Hepatitis B Virus (HBV), Hepatitis C Virus (HCV) or syphilis infection. Subjects with evidence of hepatitis B virus clearance may be enrolled. * History of other malignancy; Exception: (a) Subjects who have been successfully treated and are disease-free for 3 years, (b) a history of completely resected non-melanoma skin cancer, (c) successfully treated in situ carcinoma, (d) CLL in stable remission, or (e) indolent prostate cancer requiring no or only anti-hormonal therapy with histologically confirmed tumour lesions that can be clearly differentiated from lung cancer target and non-target lesions are eligible. * Patients with symptomatic brain metastases. * Severe symptomatic arrhythmias (excluding atrial fibrillation) * The following cardiac abnormalities: * Corrected QT (QTc) interval ≥480 msecs (Arm 2) * Arm 4: LVEF \<50% * History of acute coronary syndromes (including unstable angina) within the past 6 months * Coronary angioplasty, or stenting within the past 24 weeks * Class III, or IV heart failure as defined by the New York Heart Association (NYHA) functional classification system * History of known arrhythmias (except sinus arrhythmia and atrial fibrillation) within the past 3 months * History of myocardial infarction within the past 3 months * Uncontrolled medical conditions (i.e., diabetes mellitus, hypertension, uncorrectable electrolyte abnormalities (including magnesium etc), psychological, familial, sociological, or geographical conditions that do not permit compliance with the protocol; or unwillingness or inability to follow the procedures required in the protocol. * Pregnant, lactating or actively breastfeeding females. * Arm 1: Treatment with systemic corticosteroids or other systemic immunosuppressive medications (including but not limited to prednisone, dexamethasone (\>2mg), cyclophosphamide, azathioprine, methotrexate, thalidomide) within 2 weeks prior to registration, or anticipated requirement for systemic immunosuppressive medications during the trial * Patients who have received acute, low-dose, systemic immunosuppressant medications (e.g., a one-time dose of dexamethasone for nausea) may be enrolled in the trial after discussion with CTC. * The use of inhaled corticosteroids and mineralocorticoids (e.g., fludrocortisone) is allowed. * Low-dose supplemental corticosteroids for adrenocortical insufficiency are allowed. Doses of ≤2mg dexamethasone or equivalent (e.g. ≤12.5mg prednisolone) are allowed. * Arm 1 (combination therapy involving pemetrexed only): Presence of third space fluid which cannot be controlled by drainage before or during initiation of pemetrexed therapy * Arm 1 (combination therapy involving pemetrexed only): * Bilirubin \>1.5 times the upper limit of normal * Transaminases \>3.0 times the upper limit of normal (ULN), except in presence of known hepatic metastasis, wherein may be up to 5 times the ULN * Arm 1: Patients cannot receive MPDL3280A (Atezolizumab) monotherapy if their immediate previous line of treatment has contained immunotherapy targeting PDL1 or PD1 with or without chemotherapy, see Appendix 6 (3). * Arm 1: Patients cannot receive MPDL3280A (Atezolizumab) in combination with chemotherapy if their immediate previous line of treatment has contained immunotherapy targeting the PDL1 or PD1 given in combination with chemotherapy, see Appendix 6 (3). * Arm 2: Previous BRAF inhibitor therapy. * Arm 2: Patients taking medicines known to prolong QT interval 2 weeks prior to registration. Use also not permitted while on trial