First relevant point: Was the save requirement met?
This factor may very well affect the desired behavior! Generally, we don't want to have to manually end completed levels, but having the option can be nice when trying to optimize. We're not always trying to optimize, and probably not trying to optimize most of the time, so while we want to be able to accommodate this use case, the defaults should probably assume the player would like to move on when the level was successfully cleared.
Obvious end states (regardless of save progress):
There are no lemmings remaining.
There is no time left.
Only zombies remain.
All remaining lemmings are blockers with no way to free them (note: this specific case may be a niche for auto-nuke since they don't move and it's the only possible move).
Potential other case to consider (trivially-detectable soft-locks):
Too many lemmings have been lost.
Further thoughts:
In general, when one of these end cases is reached, if the save requirement has been met, the level should end unless the player explicitly chooses otherwise in the settings menu; if not, gameplay should pause or continue (or have an option), see specifics. Since we have the option to rewind, having the level forcibly restarted is no longer the obvious choice it once was. For clarity: the instant the save requirement is met is NOT an end state and should NOT auto-end; it's merely a milestone that affects what behavior we want to see when the level would end through other means.
When we have the option to pause, continue, or end the game: I think the player should have the option which one to prefer. If they prefer continuing, specific cases should force pausing (specifically, when physics can no longer meaningfully advance; i.e. the physics are unchanging).
There are no lemmings remaining. Should probably block further physics updates to reduce rewinding; there's no benefit to allowing the game to progress in this state. But, not ending the level means that you can rewind from this state, unlike the current behavior where this case always ends the level.
There is no time left. I think it's reasonable to want to pause or continue in this case. Should probably be an option. May want to consider combining with the other "soft-locking" case, where the save requirement can't be met due to losses.
Only zombies remain. If you pause in this scenario, there IS a reason to want to resume, as you may wish to watch the movement patterns of the zombies.
All remaining lemmings are blockers with no way to free them. I'd actually say this specific case should result in an auto-nuke and then proceed to the case There are no lemmings remaining to determine further behavior. No way to free the blockers = no walkers or bombers remaining. We want to auto-nuke since technically, the nuke could free one of the blockers which probably won't get it to the exit, but in theory it could.
Too many lemmings have been lost. It may be worth having an option for, and it's arguably a similar case to time up. Still, though, I think there's arguably a major reason we might explicitly not want to pause in this situation even when we would want to pause in other conditions: replay insert mode. When you have stuff happening in multiple spots on the map, sometimes it's convenient to just completely ignore all but one part of it, do what you need to do there, rewind and replay insert.