I only knew about Fritz Lieber's Lankhmar stories through the "Inspirational Reading" sections of the 1ed Dungeon Master's Guide and the Nehwon mythos of the original Dieties and Demigods. It was always interesting, but it wasn't until I read the Mongoose RuneQuest Lankhmar supplement that I had really caught the bug and wanted to give the books a whirl. Last week, I downloaded Swords and Deviltry off of the iTunes bookstore (alas, they don't have The Dying Earth series) and was formally introduced to some of the greatest thieves in fantasy history.
I loved the book.
For my eighth birthday, I received The Hobbit and started down the fantasy path. My aunt got me the Chronicles of Narnia and The Once and Future King, but I really liked the Tolkien side more. TSR started putting out the Dragonlance and Forgotten Realms novels and I really stopped reading fantasy when I outgrew that crap. I picked up some Warhammer Fantasy novels over the last few years, which I considered fun, throwaway reading. Nothing great, but fun.
Fritz Lieber's Lankhmar books are really great reads for D&D players and referees. Maybe some of the new-school players might want something more "epic" or "heroic," but for the most part, the concept of adventurers (not heroes) who basically do the right thing for sometimes the wrong reason appeals to the kind of people I play with a lot of the time. Yeah, some guys really like to try to play the boy scout paladin, but most players are pretty much into self-improvement, loot, and glory.
Having finished Swords and Deviltry, I can see the influence the series had on the game. And I also see how it can maybe steer you as a player and DM to a different place. I recommend the books wholeheartedly. Check them out if you haven't already.