To me, it seems like to be more of an issue with the drive than the recorder's firmware. Unfortunately, the LVW-500x series have been known to give early failure (more so for recording), however in some cases it is generally a result of dust building up on the laser lens. This forum even has a huge thread covering the LVW-5005.
For a start, I would recommend running a dry-based laser lens cleaning disc in it. If you can easily get hold of high alcoholic cleaning fluid, you can try a wet/dry disc instead, but first ensure the cleaning fluid does not leave any residue by placing a drop on the shiny side of a disc and checking if it leaves any residue when it dries up. If a cleaning disc does not help, I would recommend bringing the drive back for repair/replacement under its warranty.
On the other hand, if only that rented disc gave issues, I would just assume it to be a faulty or picky disc, even though your Samsung player was capable of playing it. For example, while your Samsung player may be picky reading some media (which your Lite-On can play), there is a good chance you'll find media that works the other way around also.