Well the Grease is easy enough, LM refers to Lithium Matrix that the grease base soap is based on. Back in the 80's you could buy it at your local motor factors, as Castrol LMB , ( Lithium Matrix Base), now it's just Castrol LM. Don't mix it with any other type of grease, some base soaps can react badly and turn solid.
Basically if you are overhauling an old C5 gearbox then clean all the old grease off the gears and bearings and use the Castrol LM grease you can get from Halfords or any local motor factor, it's compatible with any residual LMB.