No. We know male and female Time Lords/Ladies exist because Romana was a Time Lady.

Therefore a male time lord does not transmogrify into a female time lady.
Want a Time Lady? Create a new character. Don't pull this subtle transexual bullsh*t on us and tell us it's "normal" for that species.
No it isn't. It's completely abnormal.
I agree!
Gallifrey (Do I have that right for Dr Who’s planet?) was supposedly destroyed during the time of an earlier Dr Who incarnation (To heretics like myself a past series! How past?) So it’s reasonable to assume from a SciFi respect-the-canon perspective that at least some of these time & space continuum hot rodders could have dodged that particularly anti-planetary bullet. You would have your Time Lady and remember Dr Who is not his real name
https://en.wikipedia.org/wiki/The_Doctor_(Doctor_Who)#Name
Call her Dr What or Where or Why!
But No!
Do the Dr Who is a LGBTXHSOETEMGH(&% (Did I get them all?)
Got to keep those snowflakes from melting!
It killed my wife’s interest in Dr Who & she’s a long term fan!
Romana was one of my favorite characters back in the day. They could have cast a great actress in that role, and I would have watched every second of it and be clamoring for more.
Instead we get this unwatchable gender-bending slop. Nuts to them. I refuse to watch it, and I hope it goes down the tubes.
You also have The Master/Missy - they’re the same person. So, it was already done!