α-ethylidene-δ-vinyl-δ-valerolactone (EVL), an intermediate derived from carbon dioxide (CO2) and 1,3-butadiene, is an important lactone to utilize CO2 as a feedstock, while L-Lactide (LLA) is a bioresorbable monomers widely used to prepare poly-L-lactide (PLLA). In this contribution, we synthesize polyesters from EVL and LLA using 1,5,7-triazabicyclo[4.4.0]dec-5-ene (TBD) as the catalyst. Following the “scrambling polymerizations” mechanism, EVL units are incorporated into PLLA backbones with 100% ring-opening polymerization selectivity, resulting in liner poly(EVL-co-LLA) with two functionalizable C=C double bonds in every EVL unit. The obtained polymers have number average molecular weights of 3.4-20.7 kg/mol and EVL contents up to 27.6 mol%. The preserved C=C double bonds from 1,3-butadiene in the obtained polymers are ready for further modification. After photoinitiated crosslinking with dithiols, the polymeric networks are transparent and have a glass transition temperature of 26.4 °C which endow them with shape memory properties with recovery temperature close to body temperature. This method offers a straightforward approach to synthesize polymers from CO2, 1,3-butadiene and LLA, and the obtained poly(EVL-co-LLA) network have potential applications in the biomedical field.