I have seen many drives work, although I would try to stick with the same brand of mechanism as was originaly in the case. I would do this to try to avoid some compatability problem. Once you pull the drive out of the case you will find the real manufacturer of the CD-RW. All lacie does is put it in a pretty case.
the enclosure is just that, an enclosure. It's only a passthrough that changes the ide bus to firewire. Nothing special, any ide burner should work in the enclosure.