Space Audyssey

From the way I understand it without looking it up, I remember a looong time ago going on Doctor Who wiki and learning about gallifrey lore. But I think before gallifreyans started medaling with time, there were witchy soothsayer ladies (forgot their names, they were in some recent doctor who episodes,sorry) that basically ruled gallifrey in the dark ages. But then when Rassilon and Omega started changing things, and time lords became a thing, the witches left to another planet and then I think one of them cursed the time lords with an inability to reproduce. Buuuut, they did come up with a way to sort of reproduce, which was a process called Looming. It was some sort of machine mechanism that by using DNA , they could do it I guess.

But of course these are in some of the books and not in actual episodes so I think they're trying to change this.

Although the rani is right that they can't sexually reproduce, it's just another form of reproduction. However, since gallifrey is gone, then the looms are also gone, so any time lords left now can't do it.

I guess without the Looming being canon, it could also be possible if the doctor sexually reproduced with someone, and the child grew up and sexually reproduced with someone all before the curse or "genetic explosion" that they talk about now. And the Doctor is extremely old so I wouldn't be surprised if he had a very different life before time lords were supreme. And even though the doctor may have been the first timelord (because timeless child plot), that doesn't mean that he/she/they couldn't reproduce before said explosion.