How do I install a receptacle box in lath/plaster wall?
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.)