Honestly, the 13 life limit was a bit of a mistake. It served the story purposes of The Deadly Assassin, sure. But it was obvious, even back then that the Doctor will continue to regenerate. Classic Who even put in precedents allowing Time Lords to get another set of 13 lives.
When the time comes, the Doctor is going to live past his thirteenth life. We will see a 14th Doctor, we will see a 507th Doctor and so on in that order.