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)
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* 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.
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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..