Assuming you’re using a noncustodial wallet, they’re not IOUs. The btc isn’t backed by anything, you have full possession of it. I’ll try an analogy, hopefully it’s helpful.

Bitcoin on lightning is kind of like bitcoin loaded on a bullet train. Once it’s on, it can go anywhere really fast, but you can only get it off at a station (going back to base layer).

And while it’s on, it can change owners any number of times