Ben Yagoda considers the resurgence of the word when used tongue-in-cheek to refer to "lady parts" or "lady politics":
One definition in the OED says, "Originally: a woman of superior rank or standing in society; … In later use more generally: a woman." Even in the "later use"—basically, the 20th century—it still carried with it some sense of its exalted past, however faint: in songs like "Lady Be Good" or "Luck Be a Lady," in Ladies Home Journal, in college team names like the Lady Wolfpack and the Lady Volunteers, in Lady and the Tramp, and even in Jerry Lewis’s "Be a nice lady!" Then there was that weird period when a hippie would introduce his girlfriend as "my lady." The soundtrack to that time was Kenny Rogers’s song "Lady" (opening line: "Lady, I’m your knight in shining armor and I love you") and Frank Sinatra’s album L.A. Is My Lady.
Then came feminism and Marilyn French’s 1977 novel The Women’s Room, the iconic cover of which is pictured above. The OED has a 1996 quote from The Guardian: "Only a few months ago I was reprimanded for addressing a female person as a lady. ‘I am not a lady, I am a woman,’ she replied. My mother would find this quite baffling and so do I." Now, even though lady and ladies have come back, they are inevitably surrounded by implied quotation marks, sometimes faint but sometimes really big.
In that way, it's similar to the resurgence of "girls":
Backing up around 40 years, that word was one of the first casualties of the women’s movement.
Just as you say about lady, it minimized women, but without any irony: A male boss would refer to his 50-year-old secretary as "the girl," to his wife’s friends as "the girls," and so on. The feminist reaction was definitely justified, but sometimes went a little far, as in the classic Doonesbury comic strip where someone announced the birth of Joanie Caucus’s daughter by saying "It’s a woman! A baby woman!"
In the last couple of decades, girl has gotten its mojo back, sometimes in the self-conscious and ironic ways you’ve noticed in lady (there may be some of this in Girls itself, which is nothing if not knowing), but sometimes completely straight. Among my (college) students of both sexes, it seems normal and unmarked to refer to females as "girls." Not long ago, when I heard a colleague mention "a woman in my class," my immediate reaction was that he was talking about a continuing-ed student in her 70s. He wasn’t—it’s just that he’s a child of the 70s.