Welcome to the forum.:flower:
Unfortunately everything is different between those two drives. The hardware required to burn a DVD at 24x is much upgraded from the older hardware that was only capable of 18x. This includes the chipset, which controls most everything that the drive does. Firmwares are written to specifically work with the drive's hardware. The last Lite-on drive to use the Mediatek MT1898LE chipset that's in your drive was the LH-20A1H back in 2007 I believe.
The DRW-24B3ST actually is a 24x Lite-on drive inside. Sorry.