Lavia would be a fantastic signing for Palace along the Eze/Olise lines, but he'd be a great signing for anyone who was cool with him needing a year or two to really start to click, imo. He and Cheick Doucoure would give them a couple ballers in the center. I'd just not want to expect too much from him yet, he's 19 and was exposed a lot at Southampton this year -- which was not entirely his fault, but he's not a fix-all.
I like his potential a lot, but I don't think you want him with the expectation he is gonna be more than a promising piece next year. Think he needs to be in a relatively set midfield where he can grow into a spot, rather than be the man at this point. But you absolutely sign him if you can -- he also counts as homegrown.
Could also be totally wrong and it was just the Southampton squad and situation (coaching and table) that held him back and he's ready to explode.