I’m convinced that some of the levels were deliberately unsolvable… get from one side of the screen to the other over a big chasm but you’ve got one exploding guy and one brick laying guy.
Maybe if I tried to play it again I’d realise that it was my limited 10 year old mind after all!
Most important tricks: blocker is released when terrain below it is removed, builder that hits terrain reverses direction, and multiple builders in a row can make staircase thick enough to be impassable from the other side.
The terminology is that the brick laying guy is a "builder" and the exploding guy is not actually a job - you're just killing him. (Then "exploder" is a job in Lemmings 2.)
In Lemmings 2 it was an important mechanic that blockers would stop blocking if you removed the ground underneath them, since by doing that you'd get credit for saving them instead of killing them. It tended to defeat the concept of the blocker, but I suspect the same was true in the original.
But in the game the lemmings don't commit mass suicide, at least if the player is any good. Worst case, some lemmings are left behind for the common cause.
The sensational Amiga puzzle video game called "Lemmings" helped perpetuate the idea, too. :)