Going upon your findings, I hacked my version of LemEdit to bypass the check and had LemEdit always run in compatibility mode.
To my surprise, it works! I was able to get the mouse working after the change. HOWEVER...
1) Although LemEdit now respond to the mouse, its response is very sluggish, at least on my particular machine. It required extreme movements for me to get the cursor to move a small distance. So usability is still very poor, but still, better than no mouse at all.
2) It seems to work best if you run LemEdit from a Command Prompt window. If you try to run LemEdit directly by double-clicking from a Windows Explorer window, it will run and it will even show the "compatible mode..." message, but the "hardware timer" line will still fail every now and then. This might also just be specific to my machine.
So anyway, we now have a start towards a possible solution in getting LemEdit to work under XP. But just beause I got it to work on my machine doesn't necessarily mean anything, so all of you should try it out and see whether it works on your machine or not, and how usable your mouse was if you get it to work.
The hacked version of LemEdit can be downloaded at
http://www.geocities.com/guestlevels/lemmings/lemedit2.zip. I purposely renamed the program to lemedit2.exe just in case it works worse on your particular machine. You definitely should keep your original copy of lemedit.exe around just in case.
I also have not yet tried it under DOSBox to see what happens.