In my previous comment, I meant to say, "there has always been a distinction **between** "Lord" used as a prefix..." It was mangled during editing.
On the contrary, I think a woman should still be Lord Chief Justice because it sounds better, and I don't see why a female holder should have an inferior sounding title.
Which of the other titles would you change? "Lady Speaker", "Lady High Admiral", "Lady Mayor", or any of the other examples David gave above? Or if we are not going to have "archaic" (or as some would call them, traditional) titles, why use the prefix "Lord/Lady" at all? It could be simply "Chief Justice", etc.