I'm not familiar with that mechanism but generally speaking grease or oil on exposed moving parts is a really bad idea since dust and other detritus will get embedded. All I do for my slide mechanism rails (we're hydraulic) is to pressure wash them. There are some "dry" lubricants that should be okay.
If your mechanism is completely enclosed, you will have to figure out what to disassemble to gain access. Last (or first) resort is call Winnie Owner Relations.