DRW-24B1ST with firmware 1.04 are LiteON iHAS124/324/524 B clones.
DRW-24B1ST with firmware 1.03 or lower are LiteON iHAS124/324/524 A clones.
They're both based on Mediatek chipsets, but you can't crossflash between A drives and Bdrives - the two series are based on different Mediatek chipsets/hardware. To avoid any doubt, that means you can't flash a DRW-24B1ST 1.03 drive with with firmware 1.04 or vice-versa!
Therefore, in your case you can crossflash your DRW-24B1ST 1.03 to a LiteON iHAS524 A drive.
Make sure you always backup both your EEPROM and Firmware before attempting to crossflash.
What info are you after?
If what you're asking is if its possible to crossflash an DVR-116D to a LiteON then the answer is NO. The best you can do is to crossflash it to a DVR-116L (aka DVR-A16J). That would enable DVD-RAM burning support and LabelFlash.