My brother and I can both have game accounts and use the same computer, no problems right?

No problem as long as you have separate LFS folders.

Well, AFAIK you don't even need seperate LFS folders. You just have to switch the current player in the "Players" section in the options menu. But you may want to consider seperate folders anyways, otherwise you'd have to enter the password all the time.

What do you mean by folders? Two separate games?

Yeah, two seperate installations of LFS. While this variant costs way more disk space, it's also easier to maintain IMO.

You could setup two different partitions, so everyone has his own windows