You can probably find canned lychees. I really like them. I have also had them fresh and those were good, but I didn't think they were worth the difference from the canned ones. You could also ask, when you are at a Chinese resto if they serve them. Then you wouldn't be stuck with a whole can, if you dislike them. Of course, a whole can might cost less than a dessert at a resto.Neither am I. I always see odd or unusual fruits that make me want to pick them up. But since I don't really eat a whole lot of fruit, I pass them by because I'm afraid I'll hate it and I'd just be wasting my money.
As for persimmons, I've never tried one.
There's one fruit I've always wanted to try and that's Lychee. But I've never been able to find them anywhere.