It's an interesting question, and one that many Forum members have endeavoured to answer over the years with their own custom level packs.
I'd suggest, it depends largely on how you define "sequel".
For example,
Oh No! More Lemmings can either be thought of as an expansion pack or a sequel, depending on perspective. It was released
as an expansion pack originally, so that's technically the correct way to think about it, but since it did include brand new tilesets and a significantly more difficult level design style, perhaps this qualifies it as a "sequel".
From that point of view, then, "Lemmings 3" (or maybe "
Yippee! Even More Lemmings") could be a pack of 100 - 150 levels featuring only the classic 8 skills and around 4-5 new tilesets.
Or maybe
Lemmings 2: The Tribes was more of a true sequel, in the sense that it took more significant strides away from the first game and introduced new features, new skills and new tilesets, yet kept some important features from the first game exactly the same - we'd need to examine the common factors that make it similar, so that a third instalment could also keep these and be a true sequel, in this particular sense of the word.
L2 keeps the same sprite animations and 8 skills from the original, the same concept of "guide lems to an exit", and continues to use a panel for control, but almost everything else is different.
So, from that point of view,
Lemmings 3: New Frontiers (for example!) could feature the same sprites again and the same gameplay concept, but streamline the skillset (or maybe even add more!) and improve further on the panel design. Everything else is up for grabs - we'd definitely want new tilesets, and maybe the "tribes" concept from L2 could be further expanded upon, maybe by having lems exploring other planets.
I also imagine that L3 would have a more comprehensive multiplayer setup, bringing it into the new gaming era.
The possibilities are many, but this is my take on it anyway