Regarding lawsuits on this topic, there is an inexhaustible number where every court into which such suits have been offered, they have eventually been tossed for lack of standing. “Who” has standing to sue has not been determined.
Not only that, this kind of lawsuit would be a PR disaster for the Democrats, especially if Cruz won the election. I do not see anyone suing over this except maybe some crazy ring-wing nuts. ;-)
Cruz us eligible and if he runs, he has my vote. Don’t really care were he spent his life as a baby.