In reactions with polar mechanisms, Lewis acid catalysis often involves binding of the catalyst to Lewis basic heteroatoms and withdrawing electron density, which in turn facilitates heterolytic bond cleavage (in the case of Friedel-Crafts reaction) or directly activates the substrate toward nucleophilic attack (in the case of carbonyl addition reactions).
In Diels-Alder and 1,3-dipolar cycloaddition reactions, Lewis acids lower the LUMO energy of the dienophile or dipolarphile, respectively, making it more reactive toward the diene or the dipole.