The LC uses the edge connector for fan and/or speaker, IIRC. The LCII moved to pin headers, so you'd need to swap other LC II components to get everything connected (i.e. you can't use LC speaker and fan with an LCII board, or maybe you can since the edge connector is still there???) Other than that, the board dimensions are as near as makes no difference close enough, so the case swap should be no-problem doable.
The LCIII board moved components around, making the dimensions slightly different, so the fan placement might be different… Not sure on that one. Moving an LCIII board into an older case might prove problematic, based on photos of the boards.
Maybe relying on Cunninham's law might draw in a complete/correct answer here
I have found that a drop of isopropyl alcohol removes hot glue incredibly easily. (The glue even stays in one piece!) When I am desoldering these analog board capacitors, I remove the glue with alcohol first, and they pop right out with minimal effort.