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.