There has to be something behind the lath. Brick maybe? At least I’ve never seen a self-supporting lath and plaster wall.

sandk is right. There has to be something there supporting the lath at least every 16 inches. That plaster would have crumbled away over the years from seasonal changes in the lath, otherwise.

And, without anything back there, no, you cannot hang a wall system from it. That snaptoggle with be spanning--at the most--2 strips of lath, which have no structural integrity of their own.

The longest span of the closet wall is 47" wide on the back wall - from the few pilot holes I've drilled, an electronic stud finder (which I know doesn't work well on plaster walls), and a tap test - I can't find anything solid behind the wall except for at the edges. I'll continue to investigate and possibly look at some other options. Thanks!