You have a hydraulic slide mechanism. Which is different that the Schwintek the other people are talking about.
There are two different type of slide mechanisms used on the Solitude (and other trailers). They are very different. On the 310GK, the bedroom is called a Schwintek and you can tell this type as it has slide racks one top, one bottom on each end of the slide out. This is what people above are replying to and saying do not use a greasy (or any) lube.
The other type is a hydraulic slide out and it has a rack and pinion inside the frame. This is the type used on the Kitchen and Dinning room slides in a Solitude. You can see the rack on the bottom of the slide out. One near the front and one rack near the back. As I understand it, this type you can grease without problem. Note: Other line of trailers )Like Reflections, Imagines, etc. have a similar type of slide out mechanism (with the rack under the slide), the only different is it is driven by an electric motor instead of a hydraulic piston.
Chris