I'm not going to invite a friend to a holiday for lying
May I ask what they lied about?
They said that they would go to the same holiday I am pretending to enjoy. I don't like that.
Although your friend is wrong for lying, not inviting them will only make things worse between the both of you. You should make up with them over this.
That wouldn't be a fair trade. I will be punishing them by not inviting them to my holiday.
Inviting your friend to your holiday will give you both a chance to work on the friendship.