"Person" also works in this case.
+1 for they. "Lady" seems patronizing to me - would you call someone a "gentleman"? To me, "lady" describes a woman who is "traditionally feminine" – I get that when people use "lady" today they don't typically mean "traditionally feminine," but "lady" is still evocative of a time when women were seen as delicate/demure/less than men.
"Person" also works in this case. +1 for they. "Lady" seems patronizing to me - would you call someone a "gentleman"? To me, "lady" describes a woman who is "traditionally feminine" – I get that when people use "lady" today they don't typically mean "traditionally feminine," but "lady" is still evocative of a time when women were seen as delicate/demure/less than men.