My brother and his friend were playing Munchkin Legends, and my brother helped him when it wasn't asked of or needed. He then stated that he was in the battle, and he tried to run away, even though he wasn't the one fighting or needed. He then played the Lemming Parade card so his friend had to run away. His friend and I thought that that was against the rules because my brother wasn't the one who had to run away. Is it against the rules?
No, a player may not foist help upon you.
The rules state "you may ask any other player to help you" at which point the player may accept or deny the request. There is no "involuntary" help.
In addition, in your specific case, since help was not needed, even requesting help is not allowed, according to the official Munchkin FAQ:
Q. Am I allowed to ask for help if I am currently winning the fight? The rules say I can ask for help if I'm losing, but nothing about if I'm winning.
A. That's because if you're winning, you don't need help, and a true munchkin would never ask for help he doesn't need. Unless a card says otherwise (and a couple do, for their own weird reasons), you may not ask for help if you are winning a combat.
Source: Official FAQ
Please keep in mind the pan-ultimate rule of Munchkin (which should be adopted for every game): The owner decides any unclear ruling issues.
Also, your brother couldn't have played the card, since he wasn't the one running away.