Randomized Trial Comparing Standard of Care Versus Immune- Based Combination in Relapsed Stage III Non-small-cell Lung Cancer (NSCLC) Pretreated With Chemoradiotherapy and Durvalumab

Inclusion Criteria: 1. Body weight \>30kg 2. Recurrent or metastatic NSCLC relapsed during or after completion of chemoradiotherapy with curative intent and maintenance durvalumab for stage III disease. Patients are eligible if they receive at least two cycles of platinum based chemotherapy or radical radiotherapy 3. Tumor tissue available for biomarker testing. 4. Evidence of disease progression during durvalumab maintenance or at the end of planned treatment. Patients who have interrupted planned durvalumab treatment after at least 6 months for reasons other than toxicity or progression (e.g. patient's choice, logistic reasons, intercurrent acute illnesses) are eligible. Patients progressing during the first three months of Durvalumab are not eligible 5. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 6. Patient is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations including follow up 7. Age \>18 years at time of study entry 8. Capable of giving signed informed consent which includes compliance with the requirements and restrictions listed in the informed consent form (ICF) and in this protocol. Written informed consent and any locally required authorization obtained from the patient/legal representative prior to performing any protocol-related procedures, including screening evaluations. 9. Life expectancy of at least 16 weeks 10. Patients must have normal organ and bone marrow function measured within 28 days prior to administration of study treatment as defined below:: * Haemoglobin ≥10.0 g/dL with no blood transfusion in the past 28 days * Absolute neutrophil count (ANC) ≥1.5 × 109 /L * Platelet count ≥100 × 109/L * Serum bilirubin ≤1.5 x institutional upper limit of normal (ULN). This will not apply to patients with confirmed Gilbert's syndrome (persistent or recurrent hyperbilirubinemia that is predominantly unconjugated in the absence of hemolysis or hepatic pathology), who will be allowed only in consultation with their physician. * AST (SGOT)/ALT (SGPT) ≤2.5 x institutional upper limit of normal unless liver metastases are present, in which case it must be ≤5x ULN * creatinine clearance estimated of ≥51 mL/min using the Cockcroft-Gault equation or based on a 24 hour urine test: Males: Creatinine CL = Weight (kg) x (140 - Age) (mL/min) ---------------------------------------- 72 x serum creatinine (mg/dL) Females: Creatinine CL = Weight (kg) x (140 - Age) (mL/min) ----------------------------------------- x 0.85 72 x serum creatinine (mg/dL) 11. Female patients should be using adequate contraceptive measures (highly effective method of contraception are present in table 3 of protocol "Highly Effective Methods of Contraception (\<1% Failure Rate)"), should not be breastfeeding, from the time of screening throughout the total duration of the drug treatment and the drug washout period (90 days after the last dose of durvalumab monotherapy) or for at least 1 month after last dose of olaparib, or they must totally/truly abstain from any form of sexual intercourse. Females of childbearing potential are defined as those who are not surgically sterile (ie, bilateral salpingectomy, bilateral oophorectomy, or complete hysterectomy) or post-menopausal. 12. Postmenopausal or evidence of non-childbearing status for women of childbearing potential: negative urine or serum pregnancy test within 28 days of study treatment and confirmed prior to treatment on day 1. Postmenopausal is defined as: * Amenorrheic for 1 year or more following cessation of exogenous hormonal treatments * Luteinizing hormone (LH) and Follicle stimulating hormone (FSH) levels in the post menopausal range for women under 50 * radiation-induced oophorectomy with last menses \>1 year ago * chemotherapy-induced menopause with \>1 year interval since last menses * surgical sterilisation (bilateral oophorectomy or hysterectomy) The following age-specific requirements apply: * Women \<50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of exogenous hormonal treatments and if they have luteinizing hormone and follicle-stimulating hormone levels in the post-menopausal range for the institution. * Women ≥50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of all exogenous hormonal treatments, had radiation-induced menopause with last menses \>1 year ago, had chemotherapy-induced menopause with last menses \>1 year ago. 13. Male patients must use a condom during treatment and for 3 months after the last dose of olaparib when having sexual intercourse with a pregnant woman or with a woman of childbearing potential. Female partners of male patients should also use a highly effective form of contraception if they are of childbearing potential. Male patients should not donate sperm throughout the period of taking olaparib and for 3 months following the last dose of Olaparib. Exclusion Criteria: 1. No evidence of disease progression 2. Patients receiving any systemic chemotherapy or radiotherapy (except for palliative reasons) within 3 weeks prior to study treatment 3. Patients not pretreated with durvalumab with curative intent 4. Patients treated with non-radical radiotherapy or with non conventional radiotherapy 5. More than 4 cycles of platinum-based chemotherapy 6. Rapid progressors. Progressors within first 3 month of treatment will be excluded from this trial 7. Any clinical reason that makes the patient ineligible to receive any investigator's choice single-agent chemotherapy regimen (for patients enrolled in cohorts A and B) 8. Any clinical reason that makes the patient ineligible to receive any investigator's choice platinum-based doublet chemotherapy regimen (for patients enrolled in cohorts C and D) 9. Persistent toxicities (\>Common Terminology Criteria for Adverse Event (CTCAE) grade 2) caused by previous cancer therapy, excluding alopecia. 10. Patients with myelodysplastic syndrome/acute myeloid leukaemia or with features suggestive of MDS/AML. 11. Disease progression within the first three months of Durvalumab therapy 12. Tumor tissue not available 13. Evidence of EGFR mutations or ALK or ROS1 rearrangements 14. Performance status \>1 (ECOG) 15. Brain metastases are allowed if asymptomatic and pretreated. A scan to confirm the absence of brain metastases is not required. The patient can receive a stable dose of corticosteroids before and during the study as long as these were started at least 4 weeks prior to treatment. 16. Diagnosis of another cancer in the last 3 years, except for in situ carcinoma of cervix, breast and bladder or skin carcinoma (squamous or basaloid) 17. Patient with spinal cord compression unless considered to have received definitive treatment for this and evidence of clinically stable disease for 28 days prior to enrolment.. 18. Leptomeningeal disease. 19. Resting ECG indicating uncontrolled, potentially reversible cardiac conditions, as judged by the investigator (eg., unstable ischemia, uncontrolled symptomatic arrhythmia, congestive heart failure, QTcF prolongation \>500 ms, electrolyte disturbances, etc.), or patients with congenital long QT syndrome. 20. Uncontrolled pleural effusion, pericardial effusion, or ascites requiring recurrent drainage procedures (once monthly or more frequently). Patients with indwelling catheters (e.g., PleurX) are allowed. 21. Malignancies other than NSCLC within 5 years prior to enrollment, with the exception of those with a negligible risk of metastasis or death (e.g., expected 5-year OS\> 90%) treated with expected curative outcome (such as adequately treated carcinoma in situ of the cervix, basal or squamous cell skin cancer, localized prostate cancer treated surgically with curative intent, ductal carcinoma in situ treated surgically with curative intent, grade 1 endometrial carcinoma) 22. History of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins and patient with a known hypersensitivity to olaparib or any of the excipient of the product. 23. Known hypersensitivity or allergy to any component of the Durvalumab formulation 24. History of autoimmune disease, including but not limited to myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, p psoriatic arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener granulomatosis, Sjögren's syndrome, Guillain- Barré syndrome, multiple sclerosis, vasculitis, or glomerulonephritis. Patients with: 1) history of autoimmune-related hypothyroidism on a stable dose of thyroid replacement hormone, 2) controlled Type I diabetes mellitus who are receiving a stable dose of insulin regimen and 3) eczema, psoriasis, lichen simplex chronicus of vitiligo with dermatologic manifestations only in less than 10% of body surface area, well controlled at baseline and only requiring low potency topical steroids are eligible for this study. 25. Patients considered a poor medical risk due to a serious, uncontrolled medical disorder, non-malignant systemic disease or active, uncontrolled infection. Examples include, but are not limited to, uncontrolled ventricular arrhythmia, recent (within 3 months) myocardial infarction, uncontrolled major seizure disorder, unstable spinal cord compression, superior vena cava syndrome, extensive interstitial bilateral lung disease on High Resolution Computed Tomography (HRCT) scan or any psychiatric disorder that prohibits obtaining informed consent. 26. Patients unable to swallow orally administered medication and patients with gastrointestinal disorders likely to interfere with absorption of the study medication. 27. History of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans), drug-induced pneumonitis, idiopathic pneumonitis, or evidence of active pneumonitis on screening chest CT scan. History of radiation pneumonitis in the radiation field (fibrosis) is permitted. 28. Positive test for HIV 29. Patients with active hepatitis B (chronic or acute; defined as having a positive hepatitis B surface antigen \[HBsAg\] test at screening) or hepatitis C. Patients with past hepatitis B virus (HBV) infection or resolved HBV infection (defined as the presence of hepatitis B core antibody \[HBc Ab\] and absence of HBsAg) are eligible. HBV DNA must be obtained in these patients prior to randomization. Patients positive for hepatitis C virus (HCV) antibody are eligible only if PCR is negative for HCV RNA. 30. Active tuberculosis 31. Concomitant use of known strong CYP3A inhibitors (eg. itraconazole, telithromycin, clarithromycin, protease inhibitors boosted with ritonavir or cobicistat, indinavir, saquinavir, nelfinavir, boceprevir, telaprevir) or moderate CYP3A inhibitors (eg. ciprofloxacin, erythromycin, diltiazem, fluconazole, verapamil). The required washout period prior to starting study treatment is 2 weeks. 32. Concomitant use of known strong (eg. phenobarbital, enzalutamide, phenytoin, rifampicin, rifabutin, rifapentine, carbamazepine, nevirapine and St John's Wort ) or moderate CYP3A inducers (eg. bosentan, efavirenz, modafinil). The required washout period prior to starting study treatment is 5 weeks for enzalutamide or phenobarbital and 3 weeks for other agents. 33. Major surgery within 2 weeks of starting study treatment and patients must have recovered from any effects of any major surgery. 34. Previous allogenic bone marrow transplant or double umbilical cord blood transplantation (dUCBT). 35. Pregnancy or breast feeding women