Lug nut bolt broke while trying to get tire off how do you remove it?

You may have to get a nut splitter, a grinder, or a hammer and chisel to get nut off and then have stud replaced. Hopefully the splines in the drum haven't been torn out and a new stud can be pressed in. If not, you might be running a lug nut short (which is not at all wise) or you'll have to come up with a new drum. Auto recyclers live for challenges like this.