George Nelson Roll Top Desk Greasing  

I wouldn't grease it. Binding of tambour doors is often caused by gunk accumulated in the track, case sides out of square, or excessive wear. In the case of your desk, not only are there four relatively short-radius curves the door has to make, but gravity is also working against fully opening the top. It's not a surprise that you're having trouble.
I'd start by addressing the items listed above in order. In the worst case, disassembly may be required. If you do decide that lubrication is needed after cleaning the track, use thinly-applied paste furniture wax.
Edit: Before you do anything else, though, check that the desk is not twisted by either putting a level front-to-back on the top edges of the case ends or sighting across them to see if they are parallel. If the floor is not flat and level, this could be part of the problem.

I'd drag an old taper candle around the track to lubricate the door after checking the issues the tktoo mentioned.

Thank you tktoo & sirlampsalot for the help! I will follow your advice.