The Doctor was lying because RTD is a rubbish writer. If you make the Doctor immortal, then you ruin him.
While I tend to agree (about ultimate mortality making him more interesting), the Doctor was immortal until Deadly Assassin introduced the 12-regen limit (at least according to Troughton in the War Games - we can live forever, barring accidents. And the scripted assumption in Power of the Daleks was that this wasn't the Doctor's first change).
Bob Holmes introduced the regen limit because he needed it as a plot point in Assassin, even though it contradicted the mind-bending scene in a story run earlier that year, which substatially rewritten by him.
It's doubtful that he intended it to become this big shibboleth, but fandom was coming into being at the time.