It is a good idea. I have a couple of external LG drives which are currently being used as enclosures for other drives and they work very well. And I rather like the modern compact Lite-On external enclosures and it is possible (but very tricky!) to open them up and exchange drives.
But when I tried it a few years ago I ran into problems.
Lite-On mounts the plugs directly to the circuit board, so their position is fixed. Unfortunately Samsung positions the connectors on the back of these drives (both SATA & PATA) in a slightly different position to most other manufacturers, including Lite-On. Although the bare circuit board will plug into the drive, it is offset by a few millimetres and when you try to reassemble the enclosure it won't fit.
This is a real shame as the Lite-On enclosure is much better Samsungs, which is larger, uses a multi-pin dual-voltage PSU and doesn't have an off switch.
Which external Lite-On model do you have?