This is not exclusive to ivies. Hopkins, Stanford and Northwestern and some others are very similar. In many cases you can get more in aid than you can receive from a lacrosse scholarship at those schools.
I think these schools are very generous with incomes under $100-$120k, but they are not equal to some ivies for higher incomes. With my oldest, our calculated need based aid for Harvard and Princeton was noticeably more than for Stanford ($160-$170k income). If I recall, we wouldn't have qualified for any need based aid at Duke. With my second child, the need based aid at these schools calculated to a lot more because they split the expected family contribution between all kids in college. So, if they determine your family can afford $50k for college and you have two kids in college, you get $25k more in need based aid than if just the one child in college.
One thing to be aware of is that if your income rises, you may not see much of it by the time you pay taxes and you family contribution for college goes up because need based aid will decline accordingly. On the flip side, if your income goes down then your need based aid will go up. A lot of kids won't have the grades, test scores and AP classes to get into these schools even as athletes, especially at some of the ivies, but it is worth looking into with an academic high achiever.
