Well, considering how deep that rule is burnt into the myth among fans, they'll probably address it and let the writers bullshit their way out of that corner.
IIRC both Davies and Moffat said that if either had reached that point in their run they would find a way to deal with it. BBC will not kill the Doctor permanently for a reference that was made decades ago.
The 13 lives thing seems to be more of a restriction than a biological limit. The Master was offered a new set of regenerations in the classic era and was given some during the Time War. The Doctor could say that if he found some random Time Lord device he'd live or simply say that during the Time War all Time Lords were given a larger number of regenerations due to the threat of the Daleks. A single shot seems to either kill them completely or cause a regeneration, having extra lives makes sense with that kind of enemy.