Your profile is very good (I’m a Lawrenceville senior applying to college right now with an arguably worse one), but being international and needing financial aid will make it really really difficult; I know maybe one international student here who isn’t obscenely wealthy. If you can write good essays and get a top-tier interview, though, I think you have a good shot at some schools—I know personally that Lawrenceville nearly exclusively admits athletic recruits as PGs, but I don’t believe that’s true for all of the schools on your list.
If you have any questions about Lville, feel free to reach out!