High academic that gives money is the way to go. Duke, Georgetown, Vanderbilt, Stanford.
If you include Georgetown as High Academic than you should include Notre Dame, Michigan, UVA, USC, and UNC in this list. All similar to Georgetown academically.
All great schools. Acceptance rates: Georgetown 12% Notre Dame 15% USC 16% Virginia 21% Michigan 26% Depends on if you prefer private or public.
Another important question for these Universities is do they allow you take any major or are you limited due to lacrosse?
Engineering and hard sciences are tough because of labs. Most schools won't flat out say that you can't take major X. Just that all classes need to be done by 2pm.
From my experience many science/engineering types who played college sports did summer school multiple years in order to fit all of their labs in.
