Hello there: getting into Lawrenceville as a day student is more difficult than getting into Andover or Exeter. The stats for accepted students from nearby WWP/Princeton area are top notch. Typically you need some extraordinary hook: valedictorian of your middle school, recruited athlete, URM or development case. My son attended Lville and he attended the local public schools before boarding in 9th grade.
I know a lot of his friends who were day students. They were top students at the local feeders (Princeton Charter, Stuart, PASH, Chapin, etc). A couple were Caroline Bradley scholars or had similar high level awards.
Building off this, a friend of mine from WWP told me there were over 200 applicants from his grade in our year (c/o 2023). About 7 or 8 got in—that’s around Harvard or Stanford selectivity. It’s an insane crapshoot for public school students.