When you run Lemmings 2 using the abandonia download, did you run the game via "L2-fix.com"? Otherwise you aren't running the patched version. The unpatched version has a variety of problems (though I don't remember your mouse problem being one of them), you need to run the patched version by running L2-fix instead of L2.
If that isn't it then I'm out of ideas, here are a random list of things you can try:
1) if you have any other input devices (eg. joystick) connected to your computer besides the keyboard and the mouse, unplug all of them, so you're left with just the keyboard and the mouse.
2) Try running DOSBox in windowed mode and see if there's any difference. Toggle between full-screen and windowed via Alt+Enter (ie. hold down ALT key and press ENTER).
3) I haven't actually upgraded to v0.74 of DOSBox, so perhaps you can try DOSBox v0.73 and see if it fixes the problem, though I'd be surprised if it does.
4) Maybe try a different mouse?