Ok book money is a bit light but close. Odds of someone getting a full or even 3/4 scholarship especially from the Long Island demographic are low. I think top players in the early recruiting game get about 20%-30%. Some a bit higher but I doubt many because lacrosse is not fully funded and it has so few scholarships 12.6 to be exact for a team of 40 or more. Most players who commit early receive more than those committing later(obvious). Until a NLI is signed you are free game for every school.
In regards to the Ivy parents saying that their child received a 1/2 or full ride. You cant because Ivys don't offer scholarships. They do offer some creative financing for athletes.
