We created accounts on the website to play LFS with my friends, then we tried to log in to the game, but it says "your unlock code does not match." We copied and pasted the passwords and everything, but it still doesn't work.

Did you get the unlock code via email? Is that what you copied and pasted?

The password for the GAME changed to a auto-generate,email delivered, unlock code
https://www.lfs.net/forum/thread/111994-Removal-of-WEB-password-and-GAME-password

Yes, you can generate an "unlock code" to paste into the "GAME password" field in LFS.

I know that's a bit confusing at the moment but next on my list is to update LFS and the translations.

By the way, when a new account is created, after you click to confirm your email, your new unlock code is displayed on that web page (so for that time you don't have to visit your details page and get a new unlock code sent by email).