Can I get a replacement with a iPhone 5 that is stolen but has limited warranty?

Bought the phone off craigslist. The guy ripped me off. Reported stolen. But it has limited warranty. Will apple replace it if I make up a lie? And also will they check if the phone is reported stolen?

The will most definitely check the phone's ESN, and will most likely get the police involved, as you have stolen property.

I would contact the police and file a fraud report, to cover yourself against any possible issues that may arise from the stolen phone issue.