If the Morbius incarnations are the same Time Lord he would have reached his limit before the War. Peter Davison (at the very least) would have been the last Doctor if he only had thirteen lives.

The seventh Doctor made out he was somehow more than just a Time Lord.

He seemed to have been present at the beginning of Time Lord history (helping Omega and Rassilon form the society of Time Lords and Tardis technology).

The novels extend this by having the Doctor a resurrected form of a Gallifreyan patriarch known as the Other.