I read somewhere (probably on one of the forums) that Lithium grease is a no-no anywhere for this purpose. Instead I have an old tin of bog-standard car grease dating from way back in the 1970s, it's served me well through the decades and I'm still only half way through it. Seems to do what's required, anyway.
Don't forget also pedal threads. I've had plenty of grief with those, when I've forgotten. Also crank tapers. Or is this last more controversial - some authorities say no, no grease...?