Take a look at this (long) thread about Replacement Drives for the liteon 5xxx models. (Is yours the LVW-5045?)
If you can't easily find the drives mentioned, I'd start with any working Liteon IDE DVD-RW drive; you can test it without actually mounting it inside. Some drives may have difficulty with FF/REW; all but the oldest are likely to have trouble with VCD or SVCD if those modes are important to you, but I'm not getting great results from those oldest drives on modern media on my own 5045, so I'd suggest a newer drive instead.
You won't hurt anything by trying different drives. Just unplug the unit first.