If an LLC business is owned by two persons, could one of the owners decide to bring a third person as part owner of the business?

That depends upon how the corporation is set up and what the articles of incorporation say about this particular issue. Without knowing those things, we cannot say much. But usually, a certain number of shares of stock are issued, in your case it might be 49% to one and 50% to the other, but you probably didn't even do that. So, you need to get an attorney and have the corporation dissolved if that is what needs to be done.