This trial evaluates the response of patients with stage IV or recurrent non-squamous NSCLC with LKB1 gene mutation to the combination treatment based on a PARP-1 inhibitor, Talazoparib, and Avelumab, a PD-L1 monoclonal antibody (https://clinicaltrials.gov). This evidence concerns the gene PARP1 and non-small cell lung carcinoma.