Before attempting to update the firmware, I would suggest downloading the firmware again from the Lite-On's firmware site, since the firmware failure likely indicates that the firmware you tried loading has gone corrupt at some stage, such as got damaged during the download stage or didn't write properly to CD. After you re-download the firmware, extract it from its zip file and place it on a CD-R or CD-RW. Be sure to enable disc verification if your writing software supports this as I have seen discs which appear to have been written fine return a verification error.
I have come across a few different reports of how to carry out the emergency firmware update, one like which you mentioned above. This is carried out by holding down the stop button with the unit unplugged and plugging in the unit with the stop button held down on the player's front for several seconds until the player's display shows a message to insert the disc. See this post for further details. On another thread, I have seen someone mention that the stop + power buttons must be pressed together to activate the emergency firmware update. Otherwise, if you can eject the drive's tray (assuming it will eject), load the firmware update CD, power on the player out of standby and give it a moment to see if it will carry out the firmware update process automatically. As I don't have an LVW-500x series recorder handy, I am unable to confirm which method is the correct process of initiating the emergency update.
Unfortunately, the only other way of getting it repaired is to get it serviced. If it is under a year old, you should be able to bring it back to the store you bought it from or arrange an RMA with an online store (if you bought it online) under its warranty.