Preventing ergonomic handlebar internal rubber cylinders to stick
Grease would make the rubber slip, defeating the purpose of the mechanism. And it might cause the rubber to deteriorate.

Best solution is to just throw these grips in the garbage, and get some better-designed ones. I've seen several types that use an external clamp (or two clamps) to hold the grip in place - I'm sure that would work better.

But if you're really set on keeping these grips, and don't mind getting "creative", you might be able to make an alternate locking mechanism. The expansion plugs that they use with carbon steering tubes would be ideal - except they're too big. So you want something that works on the same principle, but fits inside the handlebar. Go to the fastener section at a hardware store, and see if you can find expansion bolts that are the right size.