Update 04/08/2011: last.fm have updated their client, either use the Check for updates.. in the app or download it.

Still no scrobbling but the release notes show they’ve fixed it for Lion:

1.5.4.28012 (mac) (04/08/11)
—————————-
* Plugin fix for iTunes 10.5
* 64bit version of the plugin for iTunes on Lion

Original:
Sadly the last.fm client doesn’t autostart under Lion when you run iTunes; and there’s yet to be an official update. In fact the entire client has been rather neglected, seeing its last update in October 2010.

If like me, you’ve lost a bunch of scrobbles because you’ve forgotten to open it, you can add last.fm to your login items so it’ll automatically open when your Mac starts.

Open System Preferences then > Users & Groups; select your username and toggle to the Login Items page. Click the + and select the last.fm app to add to the list.

If like myself, you have the last.fm not show in the dock (and only the menu bar), select the Hidden checkbox.

Unfortunately there’s no iPhone / iPad scrobbling support on Lion yet, and I’m not sure how iOS 5 WiFi sync will be able to handle it..