The synthesis of bicyclic scaffolds has garnered considerable interest in drug discovery because of their ability to mimic benzene bioisosteres. Herein, we introduce a new approach that utilizes a Lewis acid (Sc(OTf)3)‐catalyzed σ‐bond cross‐exchange reaction between the C−C bond of bicyclobutanes and the C−N bond of diaziridines to produce multifunctionalized and medicinally interesting azabicyclo[3.1.1]heptane derivatives. The reaction proceeds well with different bicyclobutanes and a broad range of aryl‐ as well as alkenyl‐, but also alkyl‐substituted diaziridines (up to 98% yield). Conducting a scale‐up experiment and exploring the synthetic transformations of the cycloadducts emphasized the practical application of the synthesis. Furthermore, a zinc‐based chiral Lewis acid catalytic system was developed for the enantioselective version of this reaction (up to 96% ee).