Could this translate to "That bear is not a lion"?
Nope, that would be "O ayı aslan değil." The word order is quite important here.
A bear is not a lion: Wrong answer.
Ayi aslan degil
Why that is not a bear that is a lion was not accepted?
A comma after değil would have helped a lot in interpreting this sentence, ei, O ayı değil, aslan. How current, necessary, or proscribed would that be in Turkish?
that is not a bear?
That would be an accepted alternative translation.