The Lifetime Learning Credit is a non refundable credit. That means in order to get it, you must have a tax liability for the credit to offset. The credit can only offset up to the amount of the tax liability. 

Le me say it another way. If you owe more taxes than the amount of the credit, you will get it all. If you owe less taxes than the amount of the credit, it will be reduced to just the amount of taxes owed. If you owe no taxes, you will get no credit. 

Look at the amended return form 1040X. Line 18 is the amount of refund, if any, that you received from your original return. If you are expecting a refund from your original return and haven't received it yet, you should wait to mail your amended return until you receive the original return refund.

If you now owe based on the amended return, that amount is on line 20. If you are getting additional refund, that amount is on line 21.