Your math is actually right on. Taking away the larger Ivies with the huge endowments, the "Little Ivies" rarely exceed enrollments of 1800-2000 total or 450-500 per class. There are folks with income that don't need/want financial assistance. So a 1200 number receiving financial assistance in the form of scholarships/grants etc. is about right. 100% for all? Probably not. But if your child is academically successful (still hard to get in, lacrosse or not) it can be a much more successful future than choosing a school with a lesser reputation.
Remember that the discussion usually involves the "New Ivies", not just the "Little Ivies". The smaller schools are nowhere near the $2B endowment number (Boston College with 9,000 undergraduates and 4,500 graduate students for example is currently at $1.7B).
New Ivies Boston College Bowdoin College Carnegie Mellon Claremont Colleges (Harvey Mudd, Pomona) Colby College Colgate University Davidson College Emory University Kenyon College Macalester College University of Michigan New [lacrosse] University University of North Carolina (Chapel Hill) University of Notre Dame Olin College of Engineering Reed College Rensselear Polytechnic Institute Rice University University of Rochester Skidmore College Tufts University University of California (Los Angeles) Venderbilt University University of Virginia Washington University (St. Louis)