By Tobias Carroll Over the course of his decades-long career, Lou Reed balanced a penchant for challenging norms with a command of pop songwriting. That resulted in one of the most acclaimed bodies of work in the 20th century, encompassing both Reed’s solo work and all that he accomplished as a member of the Velvet Underground. And now, the city that acted as muse to so many of Reed’s songs is offering a deep dive into Reed’s discography. A new exhibition, Lou Reed: Caught Between the Twisted Stars, is running through next March at the New York Public Library for the Performing Arts. The exhib…