I think you would be better off using a remodeling box (with the flanges that rotate out to grip the wall) and ignore the stud altogether. With a remodeling box, you just have to cut a hole big enough for the box, whereas if you use a regular box, you have to cut away more so you have room to nail it into the stud.
The main difficulties you'll face are that you don't know exactly where the lath is placed within the wall, and that the plaster will be brittle with age.
Start by using something sharp to gouge out a small hole in the center of the spot for your new receptacle; I use the pointed tip of a drywall saw. Once you've exposed the lath, expand the hole up and down until you find the edges of that piece of lath. The other lath are going to be approximately the same size and spaced up to maybe 1/4" apart. Adjust your planned spot up or down a little so that at least one edge of the box lines up with a gap in the lath -- it's easier to cut through the plaster on its own.
Expand the hole until it's big enough for the box, then use a jigsaw to cut away the lath. Vibration from the saw can cause more damage to the wall so take it very slow and easy. (Another reason to avoid the stud: if the lath ends at that stud, you'll only have about 1/2" of it to hold the plaster in place.)
Best Answer
Is this already an existing box (just with damaged threads) if so then you can use some 1" #10 wood screws instead of the mounting screws that come with the outlet, this I a common problem I run in to on service calls (I am a apprentice electrician).
The other thing is that box you purchased is not a typical wall box instead you may want to try an 1104 box like this
And if you are mounting it to the drywall instead of the stud (common when drywall is already up) use some f-clips to support it it is hard to describe the installation in text so try this simple youtube video or you can use a rework box such as this as they are much easier to use but a bit more expensive (still under $10)
I hope this helps