Can I qualify for the American Opportunity Credit and the Lifetime Learning Credit?

You cannot claim both, it's one or the other.  TurboTax will choice which is best (usually the AOC).  If your income is low enough for the LLC, it is also low enough for AOC.

If you are eligible, you have answered  something wrong, in the interview. But, a lot of people are just not eligible. See https://www.irs.gov/Individuals/AOTC

https://www.irs.gov/newsroom/american-opportunity-tax-credit-questions-and-answers

 https://www.irs.gov/individuals/llc

You can use this IRS tool https://www.irs.gov/help/ita/am-i-eligible-to-claim-an-education-credit

The American opportunity tax credit (AOTC) is a credit for qualified education expenses paid for an eligible student for the first four years of higher education. The credit is  up to $2,500 and 60% is non-refundable (used to lower tax liability)  and 40% refundable.  You can only claim either one of the credit.  You can choose what's best for you.

To be eligible for AOTC,:

1. The student must enrolled in qualified  university or college to get  a degree or diploma.
2. Enrolled at least half time for at least one academic period beginning in the tax year.
3. Not a graduate student.

The American Opportunity Credit covers only the first four years of post-secondary education, while the Lifetime Learning Credit can apply all the way through graduate school.  The American Opportunity credit modified adjusted gross income may not exceed $160,000  for married filing joint. You can't claim the AOC if your modified AGI is over $180,000 for married filing joint ($90,00 all others; While, Lifetime Learning Credit phase-out amount is $139,000 for married filing joint .