Problem with Pioneer drawer sticking

I just bought a Pioneer CLD-D501 as a backup player in my garage. Although the seller claimed he'd had it working recently, the drawer mechanism is jammed. The problem appears to be with the lateral carriage that lifts the center spindle out of the way of the disc drawer.

This carriage has two plastic rails that slide perpendicular to the drawer. The rails have diagonal slots that lift the pins on the spindle assembly. The lubricant on these slots has dried up and turned brownish and clear. I a hoping just a dab of grease will solve the problem, but don't know what kind to use. What can I use between plastic and steel?

I am definitely not an expert on this subject but I can tell you that it is probably safe to use a lithium grease. Try to clean as much of the old stuff off of the surface before you apply the new lubricant.