If you and Dad have been able to get along so far, I wouldn't upset the apple cart by jumping into court immediately.
JMO, but it appears to me that the issue isn't that he took the child out to dinner with his GF, but that he lied. You even said you like his GF. I believe the issue is honesty. I can see both sides of the issue........on his, he may have felt that you would have been totally against the GF sharing dinner, to the point of fearing you would limit his time with the child. Not saying that you would have, but who knows what he was thinking when he did this.
Talk to him. You both have done well so far in communicating with each other, so don't stop that now. But make absolutely sure that when you do talk, you keep any anger or animosity out of your voice or attitude, as that will immediately put him on the defensive. He'd be more inclined to lie in the future, because he might feel that a specific situation would make you mad and refuse his request.
Instead of telling him how angry this made you, tell him how disappointed you are in him, believing that you two have had honest, open communication to this point, so you don't understand why he wouldn't tell you about it. He probably will say he didn't tell you for fear of you refusing, but make sure he understands that you might have, but only to postpone it for the time being.
Just a suggestion.........