From the Last.fm faq: Should you wish to permanently delete your account, you can do this on the Data tab (http://www.last.fm/settings/account) in your settings. From here, make sure you enter your password correctly, and confirm that you want to delete your account.
Direct removal link: http://www.last.fm/settings/account
Helpful Trick: Removing online data
Helpful Trick: Remove third-party logins
If you signed up for Last.fm using a third-party login such as Facebook or Twitter, you probably want to revoke all access from Last.fm. Click here to find out how.