Another example that I would say 0 to is, how many times did Jesus Christ come back to life? But I would say 1 to, according to the Bible, how many times did Jesus Christ come back to life? The difference between Star Wars and the bible is that there are not large groups of people who insist that Star Wars is real, so I feel safe in assuming an implicit, "According to this fictional thing". I consider the "reincarnations of the Dalai Lama" to fall under the bible category.
Or, perhaps you're implicitly talking about the world in which the Dalai Lama is reincarnated. There's not much difference to your distinction.
The correct answer is whatever is commonly excepted by Buddhists, I guess, or perhaps there is an official number. 0 would be a trick answer.