If the wall will come down by drilling then its going to fail anyway. Assuming you dont go at it with a monster drill and wrong drill bit
Its impossible to say if your going to have issues or not.
Cant you test drill with a small bit and see if you think its sound.
If so then get one in a stud and if you cannot get the other in, either use a gravity toggle if you can find one suitable, or what I would do is drill the hole very small to start. Then open it up slowly with larger bits.
If you can have the hole large enough that the screw isn't touching the plaster, but its still a small hole in the lath you may find the lath is strong enough to hold a wood screw directly.
Lathes arent particularly thick but it might be thick enough to hold that screw.
Your going to need to play with it and see what you think as you go.
Softly softly catchy monkey