Lyric discussion by squeeze my lemon 

Cover art for Lady Godiva's Operation lyrics by Velvet Underground, The

Lady godiva was censored heavily by her husband and to protest, rode the streets of her city naked on horseback. This could be what she was penalized with; a labotomy, or a murder.

That's what I've imagined. Lady Godiva of the song is such a libertine that she's given a labotomy to keep her "in her place". The ether leaks, she wakes, her screams echo on the walls and a gruesome portrait of a botched operation is painted.