I think you have a terminology problem. caddies are for removable drives. Enclosures for external drives. I have an enclosure with a DVD drive in it I use for installing software on my netbook.
A bit of investigation suggests that your Lite-On drive has an older-style, IDE interface. That means that SATA enclosures like this one aren’t going to be any good to you. Make sure that the enclosure you get lists its internal interface as IDE, like this one or this one.