You realize that you've partially cooked (actually denaturated) the meat by leaving it sit in an acid based marinade (lime juice). If you had not had an acid in the marinade, then the meat would have been raw attracting bacteria and allowing the bacteria to start on it as it started decomposition. However, with the marinade, the meat will have many of the characteristics of cooked meat. The meat will be safer (less issue with bacteria with the acid on it) but you probably don't want to wait too long to consume it. I would make sure to eat it today or tomorrow at the latest, but go ahead.
For more info about the effect of acid on meats, try this article:
http://main.kitchendaily.com/2011/06/09/ask-the-editors-will-lemon-juice-cook-meat-and-seafood/