Genomic instability is a key hallmark of cancer leading to tumour heterogeneity and therapeutic resistance. BRCA2 has a fundamental role in error-free DNA repair but also sustains genome integrity by promoting RAD51 nucleofilament formation at stalled replication forks. CDK2 phosphorylates BRCA2 (pS3291-BRCA2) to limit stabilizing contacts with polymerized RAD51; however, how replication stress modulates CDK2 activity and whether loss of pS3291-BRCA2 regulation results in genomic instability of tumours are not known. Here we demonstrate that the Hippo pathway kinase LATS1 interacts with CDK2 in response to genotoxic stress to constrain pS3291-BRCA2 and support RAD51 nucleofilaments, thereby maintaining genomic fidelity during replication stalling. We also show that LATS1 forms part of an ATR-mediated response to replication stress that requires the tumour suppressor RASSF1A. Importantly, perturbation of the ATR-RASSF1A-LATS1 signalling axis leads to genomic defects associated with loss of BRCA2 function and contributes to genomic instability and 'BRCA-ness' in lung cancers.