When did it stop working ?, was it after a software of hardware change ??
Lite-on gets a fairly good rep for CD writers, but they are still mechanical devices prone to failure like any other. If you can read CDs fine but not burn on any, then it "may" be the burning lazer thats goofed.
I suggest either testing it in a mates machine, or looking online for a replacement. In the UK you can get decent ones (such as Aopen or MSI) for around Â£20!!
You shouldn't need to update the Firmware all of a sudden like this. Firmware updates usually only imporve performance with certain media or correct existing bugs since the last update.