I just noticed that you say you paid more than $10,000 with student loans at school #1.
In that case, a better example would be: School 1 1098-T shows $11,000 in box 1 and 0 in box 5. School 2 shows $6000 in box 1 and $10,000 in box 5. You can claim up to $10, 000 from School 1 for the Lifetime Learning Credit. You can also claim you used $1000 of the school 2 scholarship to pay the rest of the expenses at school 1*, leaving only $3000 of the scholarship as taxable.
*You do not literally have to have done that. You just need to have paid qualified expenses in the same year that you received scholarships.
