Do you think it's a good idea to tell my girlfriend she has a deadline to start telling her friends we're dating?
Why give her a deadline to tell her friends?
I want to know if she's going to keep lying to me or not.
I think that you should reconsider what you are saying. Giving some one an ultimatum is not the greatest way to start a relationship.
She's already lying to me when she's telling her friends we're just friends.
Laying down challenges to your gf regarding talking to her friends about your relationship is a bad idea. Ultimatums like this will only create conflict in your relationship and undue strain on the both of you.