I think it's been suggested that the Time Lords can only be found in the main TV universe. The only reason that the Tenth Incarnation can be found in the Over There dimension of 'Fringe' is because he's a human clone of the original left behind in that world to be with Rose.
But in the Toobworld Dynamic, just about every TV dimension has its own Time Lords of Gallifrey. (Of course, in some of those TV dimensions even the Doctor was trapped in the Time War time-lock; in still others, Gallifrey never developed the power over Time, or it was destroyed by its enemies eons ago.)
Some of those TV dimensions, as has been mentioned in the past, are totally in one language or another. This is because the entire globe had been conquered by the country of that mother tongue. This is how we splain away the redubbing of established shows recorded in English into that new language. It's also how we splain away the characters who should be speaking English - such as Sherlock Holmes of Baker Street - but who are played by foreign actors speaking in their own language.
So here we have a video that shows several of these Time Lords known as the Doctor from different TV dimensions. And based on this video, all of them are basically hewing to the established events from the main Toobworld.
Of course, as I mentioned earlier, not every TV dimension has the same actor playing the Doctor at this point in the timeline. Let's face it - in the dimension in which women are the dominant species, the Doctor has been female from the very beginning. (My casting choice would have been Jean Anderson as the First Doctor instead of William Hartnell.)