The only commonly available PLA adhesive seems to be methylene chloride, which is common only because it’s part of really nasty paint stripper that actually works; I suspect you can’t buy the pure stuff anywhere.
Anyhow, I picked a pair of flat line width test plates from the PLA scrap pile, dabbed paint stripper on each, and clamped them together overnight:
Unlike acetone on ABS, paint stripper doesn’t actually combine the parts into a single fused unit; I could peel the two plates apart with some effort:
That picture shows the results of two glue-and-peel tests, with much the same result along the top and bottom edges. Some solvent damage appears as a thin white line around the edge of the glued joint, but with some care that wouldn’t be too bad.
I think paint stripper makes an acceptable adhesive for PLA, at least for joints that aren’t subject to peeling loads. You must design an interlocking mechanical joint, perhaps filled with epoxy, to withstand peeling loads, which isn’t nearly as good as the ABS option of just fusing the parts together.