He didn't lie to them. The Third Doctor also said the same thing to either Jo or Liz, but added "barring accidents." Just as a baseball game can theoretically last forever as long as you don't have a team striking out 3 times in the final inning, Time Lords can live forever as long as they don't use up their regenerations. Also, we don't know if it's "natural" to have 13 lives; we only know the High Council can grant more.
In terms of the real world, the idea of Time Lords having 13 lives wasn't invented until 1976, long after the scene in question aired.
I am aware the Council can grant more. That's why I added in naturally. The Council's means of giving extra lives is artificial.
The fact that the Eleventh Doctor has been around for nearly 200 years (He was 906 in "The End of Time", part two and is currently 1103 as of "The Wedding of River Song") supports the first post in that Time Lords can live forever "barring accidents".