Do I still qualify for the Lifetime Learning Credit with the class I took was paid fully by a grant and the university didn't send me a 1098-T form?

Whatever the amount that you, yourself paid, you can claim, even without a 1098-T.

These expenses qualify, as long as they are required to enroll in or attend a qualified educational institution:

• Tuition, if paid to the institution
• Student-activity fees, if paid to the institution
• Books, supplies, and equipment, if required to be purchased from the institution as a condition of enrollment or attendance (Lifetime Learning Credit)
• Books, supplies, and equipment, regardless of where purchased (American Opportunity Credit)

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Q. Do I still qualify for the Lifetime Learning Credit with the class I took was paid fully by a grant?

A. No. But see below.

Books are not, generally, an eligible expense for the LLC. 

There is a tax “loop hole” available. The student reports all his scholarship, up to the amount needed to claim the Tax credit as income on his return. That way, the parents  (or himself, if he is not a dependent) can claim the tuition credit on their return. They can do this because that much tuition was no longer paid by "tax free" scholarship.  You cannot do this if the school’s billing statement specifically shows the scholarships being applied to tuition or if the conditions of the grant are that it be used to pay for qualified expenses.

Using an example: Student has $10,000 in box 5 of the 1098-T and $8000 in box 1. At first glance he/she has $2000 of taxable income and nobody can claim the tuition credit. But if she reports $10000 as income on her return, the parents can claim $8000 of qualified expenses on their return.

After telling TurboTax that you didn't receive a 1098-T, answer yes to the qualify for a exception question. That will allow you to enter scholarship and expenses. When asked if you used any scholarship for room & board, enter $10,000.  That makes it taxable.