Is there a last.fm app for iOS to submit the music I'm listening to ?
iScrob seems to do what you want on the iPhone. I found after a very brief search, used it for an hour or so after answering this question and found it to be pretty neat. 

With iOS 5 I can see the track I'm playing in the lock screen and control iScrob as I would Music. 



It also displays album artwork on the lock screen:



The only disadvantage is that I can't create Genius playlists.