Most lug nuts have a bevel to self-center in the wheel's holes, so that the wheel doesn't get a chance to move back and forth, elongating the hole, and trashing the stud.
I think the cheapest I sell is about $2.50.
If it will fit (some alloy wheels don't have a lot of clearance) use an impact socket, and a battery powered impact gun. Or a four-way wrench, supporting the outboard end under your jack... Then step on the left side, and that will pop most loose.
Your counter guy should also be able to set you up with all-steel nuts.