There's a long-running genre of herding things. It is almost always made by UK developers, and is almost always about herding sheep. Usually it's mostly about moving your sheep-repelling character so as to make most of the sheep go where you want to, and usually it's played from a top-down view. Do a Google Images search for "herding game" and you will see a ton of 2D shepherd games. There have been some 3D herders as well.

Lemmings stands out because it's got you herding around something besides sheep. There was a burst of Lemmings-likes on the Amiga that had you herding various other little hapless people, I think there were even a few that gave your little helpless people weapons and made you herd them around to defeat an enemy horde.

Whistler's Brother (Br0derbund, c64/Atari - https://www.youtube.com/watch?v=lT32TokTYqc) definitely felt like it was an earlier member of the same genre despite you only having to herd one guy around. Possibly because, like Lemmings, it's from a side view.

It feels like I see a Lemmings-like (side view herder, probably without any avatar of the player) every few years. Always from teams with small budgets; nobody has figured out how to justify an AAA herder. I think the last attempt at that I heard of was Core's "Herdy Gerdy" on the PS2. (Which now that I dig up a video of I think I may need to emulate. It looks SUPER CUTE and SUPER CHILL. https://www.youtube.com/watch?v=SP24_EYuKJE)