Can I claim Lifetime Learning credit for my child that we have already claimed 4 years of the American Opportunity Tax Credit?

Yes, you are eligible to claim the Lifetime Learning Credit if all of the following requirements are met:

• You (or your dependent or a third party) paid qualified education expenses for higher education.
• You paid the education expenses for an eligible student.
• The eligible student is you, your spouse, or a dependent you claim an exemption for on your tax return.
• Your modified adjusted gross income is less than $67,000 ($134,000 if you are married filing jointly).
• The credit is reduced between $57,000 and $67,000 ($114,000 and $134,000 if you are married filing jointly).

Thank you for the quick response.  I now realize that I am not eligible because of the income.  Can my child claim the Lifetime Learning Credit on his own return instead?  Any downside of doing that way?

If he did, you would not be able to claim him as a dependent.