Sequential and simultaneous cationic copolymerizations of lactide with commercial functional epoxides: allyl glycidyl ether, glycidyl propargyl ether, and epichlorohydrin, catalyzed by a protic acid in a one-pot process were studied. Block and gradient polylactide-based medium-molecular-weight copolymers with several alkene, alkyne, or chloromethyl groups at one chain end or with gradient distribution along the polymer chain were successfully synthesized, as proven by H-1 NMR, SEC, and MALDI TOF analyses. Functional polylactides were further subjected to thiol-ene addition, cycloaddition of azide, or reaction with tertiary amine, respectively, to demonstrate the reactivity of the introduced functional groups.