A 40lb mirror is probably bigger than 16" wide, so find your studs. The mirror is going to cover up your search holes anyway, so just worry about finding them. Hint, electrical outlets are usually attached to a stud, is there one on that wall? measure 16" from each side and that will give you a place to start looking.
You might also look at getting an electronic stud finder, although I can't say I've had the pleasure of trying to use one on lath and plaster, yet.
If all else fails use the largest molly bolts you can find. the wing style works too. Just look at the packaging and you will see what each is rated for.
Have fun, and get a helping hand when you go to hang it.