I'm going out for lunch with my ex girlfriend
Why are you going to have lunch with your ex-girlfriend?
She's a great person and I like spending time with her.
There's nothing wrong with doing that.  It's totally normal to still be friends with an ex, especially if the breakup was amicable.  I hope you two have a good time!
I've set up a romantic dinner for the two us at an expensive restaurant.
It's fine to stay in touch with your ex-girlfriend if you can be friends but setting up a romantic dinner is not appropriate. Romantic dinners are typically not shared by friends and she may be confused about your intentions. You need to clearly state what the intentions of your dinner plans are.