Coessentiality networks derived from CRISPR screens in cell lines provide a powerful framework for identifying functional modules in the cell and for inferring the role of uncharacterized genes. However, these networks integrate signal across all underlying data, and can mask strong interactions that occur in only a subset of the cell lines analyzed. Here we decipher dynamic functional interactions by identifying significant cellular contexts, primarily by oncogenic mutation, lineage, and tumor type, and discovering coessentiality relationships that depend on these contexts. We recapitulate well-known gene-context interactions such as oncogene-mutation, paralog buffering, and tissue-specific essential genes, show how mutation rewires known signal transduction pathways, including RAS/RAF and IGF1R-PIK3CA, and illustrate the implications for drug targeting. We further demonstrate how context-dependent functional interactions can elucidate lineage-specific gene function, as illustrated by the maturation of proreceptors IGF1R and MET by proteases FURIN and CPD. This approach advances our understanding of context-dependent interactions and how they can be gleaned from these data.