We describe how the organocatalytic, 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU)-based lactide ring-opening polymerization can be effectively performed in a very polar solvent, N-methylpyrrolidone (NMP). Due to a low ceiling temperature, this "living" mechanism has been unreported to date, but we here demonstrate that through a combination of low temperature and repeated monomer additions (starve-fed process), this mechanism enables the generation of a plethora of multifunctional homo-and (stereo)block-poly(lactide)s (PLAs) with exquisite control of the molecular weight dispersity (typically Đ < 1.1) and topology (from linear through 4-, 6-, or 8-armed stars and up to ∼140 armed combs). They are scarcely obtainable or inaccessible through more classical synthetic methods due to the poor solubility of multifunctional initiators (polyols) in most organic solvents and monomer melts. In these precisely designed structures, branching significantly altered the nature of the materials' hydrolytic degradation, allowing them to acquire a pronounced surface character (as opposed to the bulk degradation of linear polymers). Finally, we have assessed the amenability of this method to in situ block copolymerization by using the tacticity of PLLA blocks in PLLA-b-PDLLA versus PDLLA-b-PLLA (L-LA polymerized before or after DL-LA) as a sensitive method to detect (stereochemical) defects.