Availability/Appropriateness at #23:
A not-insignificant number of mocks have him falling into the second round, and he seems a near consensus bottom-half of the first round pick. He might be taken sooner than #23, but I'd say there's a 50/50 shot that he's available at #23. He fell largely because of off-the-field issues, and a strong CB class at the top.
On the other hand, Janoris Jenkins had far greater issues and was selected at the top of the second round. I would also argue that Jenkins wasn't as good of a prospect as Peters is (though, I am aware that not everybody would agree). Jenkins was talked about as a top-15 pick without his character issues. He was arguably the most successful CB in the draft. Similarly, Peters is being discussed as potentially the best CB in the draft, and a top-15 pick without off-the-field issues.
Either way, he would not be a reach at #23, and there is a very good chance that he'll be available then. It should be noted that his stock started rising again after the Pro Day, when he was reportedly the best player there. That includes expected first round picks Danny Shelton (potentially a top-10 pick) and Shaq Thompson.
Fit:
He's got a similar build to Darius Slay. His arms are a little shorter, his hands are a little smaller, but he jumps a bit higher, is a bit stronger, and is a little more fluid. He's also, it should be noted, considerably slowelnr. Not to say he's slow, but Slay is just really fast.
The big things about Peters, though, is how he plays. He is a sticky corner who can run with anybody, and is very physical, who can play man and excels in disrupting routes. He isn't great in zone schemes, and struggles when he isn't playing press. His speed means that he is unlikely to do particularly well in the slot, but will work well on the outside. Given that we have a glut of slot CBs, Peters would be a natural heir to Mathis.
He's considered very pro-ready, with a very polished game. Given time with Austin and Oden, he could be pushing Mathis this year on the outside. With Mathis turning 35, it's hard to tell how much longer he's got before he regresses. If Mathis doesn't hold up, Peters seems a perfect replacement. If Mathis does, we could have 3 starting-caliber CBs (or 2 starting-caliber, with our long-term replacement in development).
In short, he fits our schemes, he fits our needs, fits our draft position, and he fits the timing. It would also be an eerily similar draft choice to Riley Reiff in regards to team fit.
Other options:
Regarding team needs, the other positions we need are RB, DT, and OL (OT, OG).
On the D-line, Mayhew has always liked a very specific build. Very tall, very athletic, very long arms. Suh was the small guy on the team at 6'4", with 33.5" arms (Fairley is 6'4" too, but his arms were 34.75"). Leonard Williams would be fantastic, but... that's not happening. Shelton is 6'2" (and unlikely to be available), Brown is 6'2".
Those that do fit the mould Mayhew likes:
Goldman has a lot of issues with work ethic that will likely get him taken off the Lions' board entirely. Armstead and Davis are very different, but both are predicted to be 2nd round players. Both would be fine picks by the Lions, but they'd be a big reach.
RBs have been devalued to the point of none being worthwhile in the first round.
The offensive line has a number of good prospects, but none seem to be good value at #23. There are very few sure things (although, Fisher is pretty close), and a lot of great options later on. This is definitely a possibility, but this seems like it would be an overreaction to need, rather than based on available value. That would make it a very un-Mayhew-like pick.