Anything called "ground cover" scares me. I don't plant anything labeled as such. Re: lamium, we're always run over by purple deadnettle, which is a lamium, but I didn't plant it. It's a noxious weed here.
The worst thing I think I ever planted was verbena bonariensis. I wintersowed it initially, grew it deliberately for two years. Now I've been trying to get rid of it for about 8 years. I pulled dozens of them again today.
Karen