He's already fucked her once. Let's assume that she's a hot ass stripper. That's worth at least $250 or $300. Plus, he's hung out with her off the clock for free at her place, so she feels comfortable enough to have him as a guest. All this leads me to believe this has potential for an ongoing arrangement.
We're talking about rent in Tucson, not New York City or San Francisco. Let's just say her rent is about $800 per month and he's hitting it once a week. Seems like a pretty good deal to me if she's hot and he likes her.
Yes, there are some trust issues. The phone lie is a red flag for sure. Also, he has only slept with her once and hasn't known her very long.
Pay per meet would be the best way to go, but if he pays her rent on the 1st and sleeps with her on the 1st, he's basically prepaying for 3 weeks. Not ideal, but possibly a reasonable risk if he's already fucking her and hanging out at her house, and has no reason to believe she'll ghost him. Fuck, he knows where she lives, so I'd be pretty surprised if she ghosted him, but you never know.
Regardless, whether it's pay per meet, paying her rent, or whatever, you have to assume these girls are fucking other guys. You can't let that cloud your judgment unless you are looking for a wife, in which case you are looking in the wrong place. Just be happy you are in the rotation and hopefully she's only screwing one or two other guys.
Finally, sure, you can just jerk off to internet porn and save money, but come on dude, we're not in fucking high school anymore. He found a hot ass stripper in the club who is willing to fuck him OTC. Why not invest a small amount (3 weeks advance) and give it a try. The alternative is (if she won't see him pay per meet), he's going back to the strip club, spending hundreds or thousands until he lands another OTC candidate.