When they were children, Ty Lee hated all boys except for Zuko. I want to marry Azula when I grow up, she'd said, and everyone laughed it off as a childish declaration. But later Azula said if she were a boy, Ty Lee would be a good wife. Wives listen to their husbands and support them just like Mother does for Father.
As they grew older, Ty Lee grew out of hating boys and Azula began to cultivate an interest in them. But boys were still fickle and immature, and even the ones who worshipped Azula the way she wanted would lose interest once they realized she was all take and no give.
Ty Lee, on the other hand, was more than happy to do all the giving in a relationship. All she ever wanted was for everyone to be happy, and she would go to the ends of the world to make it happen if necessary. Of course, Azula always remained at the forefront of her mind no matter how devoted she was to her latest boyfriend.
She would make a very good wife.
Ty Lee's growing affections for Azula and Azula's craving for a partner to satisfy her every whim soon led them to each other, and they became lovers.
It was, in their eyes, the ideal relationship.