The development of two divergent and complementary Lewis acid catalyzed additions of bicyclobutanes to imines is described. Microscale high‐throughput experimentation was integral to the discovery and optimization of both reactions. N‐arylimines undergo formal (3+2) cycloaddition with bicyclobutanes to yield azabicyclo[2.1.1]hexanes in a single step; in contrast, N‐alkylimines undergo an addition/elimination sequence to generate cyclobutenyl methanamine products with high diastereoselectivity. These new products contain a variety of synthetic handles for further elaboration, including many functional groups relevant to pharmaceutical synthesis. The divergent reactivity observed is attributed to differences in basicity and nucleophilicity of the nitrogen atom in a common carbocation intermediate, leading to either nucleophilic attack (N‐aryl) or E1 elimination (N‐alkyl).