He's going to try and have an affair with her by the sounds of it. The other girl is an idiot if she has lunch with him while knowing that he's still with you.
Why wouldn't you tell him what you read and that you are against him meeting her for lunch, dinner, a drink or even a cup of coffee without you joining them. You are a couple and what he is doing is disrespectful and wrong for a man to be doing when he is in a committed relationship.
You'd do well to have a conversation with him and then leaving him to her. Let him be her problem... which he will be and it will be her finding a text to yet another girl about how he's bored with her and would she like to meet up for a drink... Hell, if you leave him, and you're not smart enough to know better, it could even be you he's texting to cheat on her with you. He's an asshole... I don't know you but I know you can do better.
“The willingness to accept responsibility for one’s own life is the source from which self-respect springs.” ~Joan Didion