Lehigh and William & Mary are both in NCAA D1 (not D2). However, they play football in the FCS subdivision of D1, which gets far less media attention and fan interest than the FBS subdivision. This is the same athletic status as the Ivy League (in fact, Lehigh regularly plays Ivies in non-conference football games).
Lehigh and W&M are relatively small by NCAA D1 standards, and have relatively high academic standards. This means that in general, they are not nationally competitive in major college sports (again, this is like the Ivy League). One exception is Lehigh wrestling, which is commonly ranked in the Top 10 nationally. Last year’s matchup between Penn State and Lehigh (then ranked #1 and #5) drew almost 10,000 fans, and was one of the top college wrestling events of the season.
http://www.mcall.com/sports/college/psu/mc-spt-lehigh-wrestling-penn-state-20171130-story.html
Lehigh and W&M both quality in terms of size, spirit, good academics, and selectivity. However, W&M doesn’t have engineering (except as a 3-2 program). Lehigh might be a better fit, since it has a large traditional engineering school with a strong reputation.