No, expenses paid for a past year are not eligible for the Lifetime Learning Credit. Only the expenses specifically listed in Publication 970 are eligible.
Form 1098-T is not the final determination of expenses that are eligible for the credit. The instructions to the school for filling out box 1 on Form 1098-T are different from the instructions for the student who is claiming the credit. The 1098-T is supposed to include payments of past-due tuition, but that does not make those payments eligible for the credit.
For the benefit of other people who might read this thread, the same rule applies to the American Opportunity Credit.