Headscratchers / Allison and Lillia

• I've only seen the anime, so forgive me if this is a stupid question; is there any particular reason why Lillia couldn't be told that Travas was her father? Virtually every other named character seems to know who Travas really is, including Allison and Treize, the latter of whom explicitly swears to Travas not to tell Lillia who he really is. Why? Hell, she already likes Travas enough to be completely pro the idea of him marrying her mother. From what I remember, she doesn't seem like the kind of person to go blabbing about him to anyone else, so why don't they just tell her?