If all she did was lay by the door when she was out, that would indicate to me that she, in fact, wanted to be inside, not outside! How old is Lola? It does sound to me like she just needs attention, and I don't see how she's going to get that outside. Does she have enough toys and playthings inside to keep her busy? Also, and most importantly, does she still have all her claws? If not, that is a very strong argument for keeping her in.

If there is no disuading your mom and grandmother, I would start with only supervised visits outside to somehow let her know the boundaries of what you think is safe for her. Not that that will matter because we all know a cat will do what it wants to do when no one is looking, but at least she'll know.

Good luck and do not give up in your arguments to keep her inside. Just keep plugging away and maybe, hopefully, they will change their minds.