Reading over this as-yet-unresolved topic again, I'd propose the following:
1) "All lemmings are dead" behaviour mimics "Time's up" behaviour, playing some sort of "level failed" sound and changing the lemming count to a red "0" but keeping the level active. I think people have been wanting this for a long time, especially for "1 lemming" levels.
2) The alarm (and "level failed", if accepted) sound should be F2 optional.
3) "Pause when timer reaches zero" should be F2 optional.
4) On second thoughts, I don't think it's necessary to show a "Time's up" graphic (with continue button). Ideas around its implementation don't seem to fit nicely with the way NL works, and it would just create extra faff. What I
would propose here, though, is something which would provide a clear visual cue that something has happened, whilst also masking the wierd "bunch of exiting lemmings" thing that occurs after time has run out (which tbh has always looked like an unintended glitch or bug).
After the time has run out, a clock icon appears over the exit, like this:
5) Something that came up during a conversation on Discord: If a level's save requirement has been met, there are still lemmings in the level, and the time has run out, currently the level continues to play. Presumably this is so that players can go back to try and save more for talisman and/or challenge purposes, and whilst that's great, it does mean that players have to manually Esc or nuke the level to finish it during normal gameplay. Since they have actually completed the level, ideally it should finish when the timer runs out.