I honestly don't like Lydia being in my house. I mean, you become thane and all and it's really cool that the jarl gives you a person to watch over your stuff, but I don't bring her into combat. As a result, all she ever does is sit in my house at my little table and think about nothing. At first I must admit to being intrigued by the idea of an attractive woman in my house, but she doesn't do anything. It's kind of jarring to see.
Could you add some stuff for her to do? At least let her give you a haircut or try on different outfits, I don't know. She literally has nothing to say or do and it really bothers me. And I come back to my home every few hours to put my many dragon bones and scales away and before I leave I try to see if maybe she has some new dialog....but there's never anything.