Lemmy Koopa, or simply just Lemmy, is one of the seven Koopalings adopted by Bowser. He is the smallest Koopaling, very childlike and seems to have a liking for the circus.
Super Mario Bros. 3
In Super Mario Bros. 3, Lemmy is the boss of World 6, Ice Land. Lemmy is found and battled by Mario in the cabin of his Airship; in battle, Lemmy would ride a rubber ball around the room and use his stolen wand to generate more rubber balls, that Mario must dodge. Jumping on Lemmy's head three times results in defeat.
Super Mario World
In Super Mario World, Mario fights him in the subterranean Vanilla Dome area. In this battle, Lemmy does not attack Mario directly. Instead he simply pops out of a Warp Pipe in his chamber, along with two Lemmy look-a-like dolls. Mario needs to jump on the real Lemmy's head three times to knock him out of the end of his Warp Pipe and into the lava below, avoiding the fake Lemmys as the Podoboos bounce around the room. Also, Lemmy notably has teeth in this game, unlike his artwork.
In Yoshi's Safari, Lemmy is the first boss encountered. He has a machine with a big head that looks just like him. However, if you damage the face then eventually you'll get to damage the real thing. He has possession of the Garnet Gem. In Super Mario Bros. 3, Super Mario World, and Mario and Luigi: Superstar Saga, Lemmy’s fighting style matches that of his sister, Wendy, except he throws rubber balls instead of rings.
In Mario and Luigi: Superstar Saga, he is the third Koopaling to fight Mario and Luigi, just like how he was the third Koopaling to be fought in Super Mario World.
In battle, Lemmy can make three extra clones of himself. Mario & Luigi must attack the real Lemmy. After attacking the real one, the fake ones explode. Another attack is for Lemmy to spit fireballs, which can be deflected by hammers. After defeating Lemmy, the player gains access to face off Ludwig. In the remake, Lemmy creates his clones by using his magic wand. The clones and Lemmy spin in a circle to confuse the player. However, if the player pays close attention to the real Lemmy, the player will know which one to attack. Also, hitting the real Lemmy doesn't destroy the other clones. If at least two fake clones are destroyed, or all clones are destroyed, Lemmy will make more with his wand.
In terms of stats, Lemmy has 380 HP, 110 POW, 155 DEF, 120 SPD and 800 EXP. In the remake, Lemmy has 540 HP, 130 POW, 122 DEF, 103 SPD and 650 EXP.
New Super Mario Bros. Wii
In New Super Mario Bros. Wii, Lemmy is the boss of the World 3. In the first fight in the Tower, Lemmy uses his scepter to conjure a ball and bounce it towards the player(s)' character(s). While the ball doesn't inflict damage, the player needs to run under it it or jump on top of it to bounce over it, as it does push the player towards the edge of the ledge, and into a pit. Lemmy can be defeated by stomping on his head three times. He is fought for a second time in the Castle level. He is fought the same way, but his ball is significantly bigger. When he gets hit 2 times, the ball Lemmy stands on further increases its size for additional difficulty to damage him one last time.
New Super Mario Bros. 2
Lemmy Koopa returns as a boss in the Nintendo 3DS title, New Super Mario Bros. 2, as the boss of World Flower, he acts in the same way as in New Super Mario Bros. Wii. In his battle arena, the ground is a conveyor belt and a switch is on the ceiling. Mario can bounce on Lemmy's balls to knock the switch, which causes the conveyor belt to change direction. Lemmy has to be stomped three times in the game.
New Super Mario Bros. U/New Super Mario Bros. U Deluxe
Lemmy Koopa made his debut appearance in Mario Kart 8, and its Nintendo Switch port, as a playable racer along with his siblings. This is also his first appearance as a playable character in a spin-off game.
Super Mario Maker 2
In Super Mario Maker 2, Lemmy is an enemy that is able to be placed, he acts in the same way as in New Super Mario Bros. Wii and has to be stomped three times. If the player gives him wings, he will act in the same way as in the castle of New Super Mario Bros. Wii.
Lemmy's attacks usually consists of trying to trample Mario with his ball. In Superstar Saga, he could split himself into five different mirrored forms. However, his ball does not appear in the game. He could also breathe fire. Like Wendy, he uses decoys in battle in both Super Mario World and Superstar Saga.
Very little is known about the Koopalings' personalities other than what is seen in the Super Mario Bros. cartoons. Lemmy is considered immature, childish, and quite silly. He would rather perform in the circus, than cause Mario and Luigi trouble. He usually will mess up the simplest order, if not forget what it was. He is not as evil as most of his siblings, as he usually pulls small pranks. Lemmy simply wants fun, laughs, and to make his father proud.
Lemmy is usually seen with wobbly eyes and multi-colored hair. He is the smallest koopaling. His trademark weapon is his yellow rubber bouncy ball with star designs which he stands on. This explains his circus look. He has recently sported a yellow ponytail in addition to his mohawk. Fans usually add a small fang in the top corner of his mouth in art. He also has a padded stomach and padded feet.
In the cartoons he was named Hip Koopa and was often seen with his brother Hop (Iggy Koopa). The two of them shared most of their sentences (à la Donald Duck’s nephews Huey, Dewey and Louie) and were usually seen pulling pranks. There are two major differences between Lemmy and Hip: Hip’s hair is far thinner, and he has an overbite. They were both voiced by Tara Strong.
In the comic books, Lemmy was quite stupid but could somehow understand Larry’s picture-only dialogue. He was also a fan of Mario’s favorite comic book superhero, Dirk Drain-Head.
In Super Scope 6, Lemmy, riding a missile and chasing Mario, who is in a plane, will sometimes appear in Type A: Intercept mode and fly across the screen. If players hit Lemmy with their Super Scope, they will either recover a miss or gain points.
Lemmy was named after Lemmy Kilmister, the lead singer of the English rock band, Motörhead. 
When fought in Super Mario Bros. 3, while the other Koopalings shift to another part of the room after being stomped on, Lemmy remains stationary on his ball (probably due to limitations of the NES). In New Super Mario Bros. Wii, after each time he is stomped on, the ball disappears and he shifts around the room in the same way as the other Koopalings, and then produces another ball with his wand.
Lemmy's ponytail that he wears starting in New Super Mario Bros. Wii looks similar to Tiny Kong's ponytails.
The Prima Guide for New Super Mario Bros. Wii usually refers to Lemmy as Little Lemmy Koopa.