Yes, you should apply to several Ivy’s. They will probably be able to offer the best financial aid. By the way, are you aware that you can apply for free with fee waivers because of your family income?
Regarding EDII, I suspect you would find Colgate more generous with aid than Lehigh. However, Colgate is in a really remote, cold area. It’s beautiful though and has a super alumni network.
What about your state flagship? I would think you would be eligible for admission to the Honors College, which often means tuition would be free.
There are also one or two good schools you could attend absolutely free. When I remember the names, I will post here.
Remember to think of transportation costs. They can really add up, and it helps if there is a direct bus, train, or inexpensive plane route between your hometown and the college you choose to attend.
Again, best wishes to you.