lug stud is loose

They do make some slight oversize lugs as well once you get it off... Im assuming stock axles?

I would try a good impack first as well, see if you can zip it off...

Is it a front wheel stud, or a rear? The studs press into the flanges through the back, and are splined. If you're lucky, the splines are still ok in the flange and you can just press a new stud in and be on your way. If the flange is stripped out, you'll have to hunt down some oversized repair studs or replace whichever flange is messed up (fronts are hubs, rears are axleshafts). You may be able to rotate the flange to a point where the head of the stud will be accessible to get a pair of vise grips on so you can remove the lug nut.

If you manage to get the old stud out and the flange is fine, you can install a new stud by sliding it into the flange, put several wide washers on the stud, then install a lugnut and tighten against the washers until the head of the stud is seated flush with the back of the flange.

This is thread is old but i had the same problem today so Just in case someone else has the problem you could try this.
make sure the loose stud is at the top of the wheel with all the other nuts nearly off and the one or ones at the bottom at the bottom (depending on a four or five stud wheel) just hanging on.
Pull the bottom of the wheel out as far as you can, so the top part of the tire goes back and the loose stud ends up at an angle in the hub while you slowly lower the trolly jack or what ever jack you are using.
The weight of the vehicle will eventually rest on the loose stud trapping it at an angle between the hub hole stopping it from rotating.
you should then be able to loosen the nut by hand like i did today. then jack it back up and take off the rest of the nuts.
I Soaked the loose stud every couple of hours with penetrator the day before to give me a chance of loosening it off.