Cyanoacrylate works on PLA, but PLA is notably not amenable to solvent welding or smoothing with household supplies compared to the ease with which ABS/ASA (acetone) or PVB (isopropyl alcohol) pieces can be fused together.

It is marginally possible to fuse pieces of PLA together using ethyl acetate (sold to consumers as "acetone-free nail polish remover" or "MEK substitute"), but this is not nearly as accessible, effective, or reliable compared to other plastics.

I've always had pretty mixed luck with cyanoacrylate. It kinda works, but it's never very strong on PLA. Doesn't hold up nearly as well as a welded connection.