Homogeneity of copolymers is a general problem of catalytic coordination polymerization. In ring-opening polymerization of cyclic esters, the rational design of the catalyst is generally applied to solve this problem by the equalization of the reactivities of comonomers—however, it often leads to a reduction of catalytic activity. In the present paper, we studied the catalytic behavior of BnOH-activated complexes (ВНТ)Mg(THF)2nBu (1), (ВНТ)2AlMe (2) and [(ВНТ)ZnEt]2 (3), based on 2,6-di-tert-butyl-4-methylphenol (BHT-H) in homo- and copolymerization of L-lactide (lLA) and ε-caprolactone (εCL). Even at 1:5 lLA/εCL ratio Mg complex 1 catalyzed homopolymerization of lLA without involving εCL to the formation of the polymer backbone. On the contrary, Zn complex 3 efficiently catalyzed random lLA/εCL copolymerization; the presence of mono-lactate subunits in the copolymer chain clearly pointed to the transesterification mechanism of copolymer formation. Both epimerization and transesterification side processes were analyzed using the density functional theory (DFT) modeling that confirmed the qualitative difference in catalytic behavior of 1 and 3: Mg and Zn complexes demonstrated different types of preferable coordination on the PLA chain (k2 and k3, respectively) with the result that complex 3 catalyzed controlled εCL ROP/PLA transesterification, providing the formation of lLA/εCL copolymers that contain mono-lactate fragments separated by short oligo(εCL) chains. The best results in the synthesis of random lLA/εCL copolymers were obtained during experiments on transesterification of commercially available PLLA, the applicability of 3/BnOH catalyst in the synthesis of random copolymers of εCL with methyl glycolide, ethyl ethylene phosphonate and ethyl ethylene phosphate was also demonstrated.