It's a difficult issue to resolve.
The traditional approach is that "Lord" is effectively an adjective (I believe the technical term is a "noun adjunct") modifying the position in question. A Lord Mayor is not a Lord who is a Mayor: he is just a particularly important Mayor. "Lord" (in this context essentially just meaning "high" or "important") has been added as a modifier to all sorts of positions over the years for this reason ("Steward" vs "High Steward" vs "Lord High Steward", "Chamberlain" vs "Lord Chamberlain" vs "Lord Great Chamberlain", etc). It therefore does not change when the holder is a woman: as others have noted, there are plenty of examples of this - female Lord-Lieutenants, Lord Mayors, First Lords of the Treasury (and even there, where it looks like a noun, it's really just a contraction of "Lord Commissioner of the Treasury"), Lord Presidents of the Council (including the incumbent, Penny Mordaunt), etc.
As also noted by others, this hit a snag when female judges started to be appointed: it would be pretty bizarre for a female judge rising through the ranks to be "Mrs Justice Smith" in the High Court, and eventually "Lady Smith" in the House of Lords (originally; now the Supreme Court), but in between those being "Lord Justice Smith" in the Court of Appeal. As alluded to previously, another complicating factor is that this is both a pre-nominal title ("Lord Justice Smith") and a position ("Lord Justice of Appeal"). It's one thing to say "Jane Smith is a Lord Justice of Appeal" (just as "Jane Smith is the Lord Mayor of London"), but another to say "Jane Smith is Lord Justice Smith". This issue doesn't arise with other titles because they aren't used pre-nominally. And now with the first female LCJ, I suppose the feeling is that having been "Lady Justice Carr", and being about to become "Lady Carr of Somewhere" (presumably), it would be an oddity for her suddenly to have "Lord" in her title.
But just adopting the "Lady Chief Justice" approach and saying "Lord now always becomes Lady when the holder is female" is also not as simple as it might sound. When a Lord Mayor is a man, his wife is a Lady Mayoress. So female Lord Mayors might not actually want to become Lady Mayors: they may feel that that makes them sound like consorts rather than substantive office-holders. (No such risk exists with judicial titles, of course - the wife of a male Lord Chief Justice is not a Lady Chief Justice! - but that cannot be said across the whole spectrum.)
That said, I suspect that eventually that is the way that this will go. At some point, a woman becoming Lord President of the Council, or whatever, will ask "why do I have to be Lord President of the Council when the head of the judiciary gets to be the Lady Chief Justice?". Since the principle adopted here appears to have been that the office-holder has been allowed to choose the form of her title, I suspect that such a person will then be allowed to be known as the Lady President of the Council. And once that starts happening, I suspect it will be adopted across the board pretty rapidly.
(As an aside, I also found the "Ms Justice Russell" situation rather odd. As I understand it, the objection to "Mrs" in general is that women, just like men, should not be forced to use titles that denote their marital status. But the "Mrs" in "Mrs Justice" has never denoted marital status - female High Court judges have always used that title, married or not, and there has never been a "Miss Justice". Interestingly, yet another option has been used in Northern Ireland, where there is currently a "Madam Justice McBride".)