This subject has come up before on this site when someone (I forget who) was given the 'its me or the dog' ultimatum and i'll say the same thing this time. If a relationship has to come down to ulimatums like this is it really much of a relationship?
Maybe its time to sit back and think about the relationship you guys have together..?
However, you shouldn't have lied to her to get your own way, telling the truth in these situations is always preferable, especially seeing as us women always get to the truth one way or another...
Good luck with the situation, I hope you get it sor