Terminal-functionalized polyesters and triblock polyesters were synthesized by lipase-CA-catalyzed ring-opening polymerization of seven-membered ring lactones, i.e., 1,5-dioxepan-2-one (DXO) and epsilon-caprolactone (CL), in the bulk in the presence of an appropriate alcohol that acts as an initiator. To introduce a double bond at the chain end, 4-pentene-2-ol was used to initiate the polymerization of the lactones. The unsaturation introduced at the chain end in this way is a useful approach for synthesizing comb polymers. Two different dihydroxyl compounds, viz. poly(caprolactone diol) and poly(ethylene glycol), were used as macro-initiators. Triblock copolymers were synthesized in this way, where the macro-initiator formed the middle block. Polymers having different degrees of polymerization were synthesized by varying the molar feed ratio of monomer to initiator. DXO and CL showed significant differences in reactivity toward lipase-CA-catalyzed polymerization initiated by different alcohols as initiators. The polymers were characterized by FTIR, NMR, SEC, optical microscopy, and DSC techniques.