If you don't have a tax liability, the Lifetime Learning Credit is useless, it would not be generated since it would not be used.
The Lifetime Learning Credit is non-refundable, so once your tax liability is zero-ed out, there is no more credit.
If there is no tax liability to begin with, the credit is not generated.
The American Opportunity Tax Credit is refundable. If you were eligible for that credit, once your tax liability was zero-ed out, the remaining credit would become part of your refund.
The American Opportunity Tax Credit has more requirements, such as being an under-grad and is only allowed to be used four times per student.
Pub 970
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