Lactic acid is one of the key biobased chemical building blocks, given its readily availability from sugars through fermentation and facile conversion into a range of important chemical intermediates and polymers. Herein, well-defined rubbery polymers derived from butyl lactate solvent were successfully prepared by reversible addition–fragmentation chain transfer (RAFT) polymerization of the corresponding monomeric acrylic derivative. Good control over molecular weight and molecular weight distribution was achieved in bulk using either monofunctional or bifunctional trithiocarbonate-type chain transfer agents. Subsequently, poly(butyl lactate acrylate), with a relative low Tg (−20 °C), good thermal stability (5% wt. loss at 340 °C) and low toxicity was evaluated as a sustainable middle block in all-acrylic ABA copolymers using isosorbide and vanillin-derived glassy polyacrylates as representative end blocks. Thermal, morphological and mechanical properties of copolymers containing hard segment contents of <20 wt% were evaluated to demonstrate the suitability of rubbery poly(alkyl lactate) building blocks for developing functional sustainable materials. Noteworthy, 180° peel adhesion measurements showed that the synthesized biosourced all-acrylic ABA copolymers possess competitive performance when compared with commercial pressure-sensitive tapes.