The LH-20A1H likes to work in UDMA4 mode when possible. I think the BenQ might still only be UDMA2.
If the LH-20A1H is only negotiating UDMA2, you may have to disconnect the BenQ and LiteOn, boot up to let Windows see that neither is connected, then shut back down, reconnect only the LiteOn, and start back up to see if UDMA4 is negotiated. (The equivalent activity would be to uninstall both drives using device manager in Windows, uninstall the PATA channels in Windows, then shut down, unplug only the BenQ, start the computer, and see if Windows reinstalls everything with the LiteOn negotiating UDMA4).
If you still have issues with the LiteOn, try a different cable. If that still doesn’t work, your drivers in Windows may not be set up properly. If trying different drivers still doesn’t help, check the motherboard BIOS. If that still fails, the PATA controller on your motherboard may not work well with optical drives.