Can you take the Lifetime Learning Credit for a State Approved Private Massage School where you receive certification? We will not receive a 1098-T from them.

Possibly.  In order to claim the credit, your school must be listed as an eligible institution with the Department of Education.  If it is listed, then assuming you  meet the rest of the criteria then you can take it.  If it is not listed, then you cannot take the Lifetime Learning Credit.