The best puzzle games like Lemmings are Lemmings (2006), The Incredible Machine and ChuChu Rocket. Below are 7, each with the reason it is here — and, at the end, what filtering to puzzle costs you.
Filtering to puzzle means you want to understand something rather than execute it. It is the right filter when what you liked was the click of working out how a system worked.
What you get: The moment of understanding as the reward. Good puzzle games teach a rule, let you feel clever, then show you the rule was smaller than you thought.
What made Lemmings worth playing in the first place is covered on the full list. This page is the puzzle part of that answer, and only the puzzle part.
The PSP remake, and the cleanest way to play the original levels today.
The other great indirect-control puzzler — build the contraption, then watch it fail.
Arrows on a grid, mice that never stop moving. The same panic in miniature.
Hand out orders to a line of wind-up toys and hope the line survives.
Physics puzzles where you design the solution and then watch it hold or not.
A modern crowd-routing puzzler, and the closest thing to Lemmings anyone has made in years.
If the appeal was the pressure of something arriving whether you are ready or not.
Momentum. Puzzle games are paced for twenty minutes at a time and most of them get worse past an hour.
Specifically, these are strong answers for Lemmings that are not puzzle games, so they are not on this page:
The full list is on games like Lemmings — 10 picks, no genre filter.
Lemmings (2006). The PSP remake, and the cleanest way to play the original levels today.
No. Lemmings released on the PC & Modern Multi-Platform, but a recommendation is only useful if you can play it, so the picks above span platforms and eras. What they share is the genre and the reason.
Rarely. A friendly art style is not a difficulty setting — some of the hardest games ever made look like children's books.
In a well-designed game the piece you are missing was taught two rooms ago. If a solution only arrives by trying everything, the design is the problem, not you.
By hand. Each pick was written for the full Lemmings list first, on what the game actually does, and this page is the part of that list that is puzzle — never a genre tag lookup, which is how "best racing games like Super Mario 64" used to be a page on this site.
Or read the puzzle guide for where to start in the genre generally.