Couple things you can try.
From your pics, you can see where the lugs are rusted, which prolly caused this issue. Before you do anything further soak the inside of the nuts / face of the lugs with PB Blaster or WD40, Several applications over a 24 hour period. Next obtain a female nut extractor or extractor set - sometimes referred to as lug nut extractors, some examples here (
https://www.amazon.com/lug-nut-extractor/s?k=lug+nut+extractor ).
https://www.amazon.com/lug-nut-extractor/s?k=lug+nut+extractor
You will need to make sure that the extractor you use has an inside diameter that will work with what is left of your lug nut and an outside diameter that will fit inside the lug nut opening in the wheel. If you can borrow these from a friend or shop, you can try out several until you find the one that best fits. It may be necessary to carefully heat the nut (so as to not damage the wheel or expand the lug too much to further bind it to the lug nut. A fine tip Acetylene or Oxy / Acetylene torch will concentrate the heat in a small area.
BTW, Whenever swapping or rotating wheels, make sure you use a healthy amount of anti-seize on the lug studs and you will not run into this problem, that is, unless some idiot uses the wrong size socket (like an SAE socket close to the metric size required).
Good Luck