Wait a minute, this bastards slick with his words!
Nah, that felt utterly robotic.
If he's really slick, he would say "I suppose I could go out for lunch with you lot, but why would I if there's the most beautiful lady standing right next to me? Hey Senpai, let's go to lunch, and I'm buying. I can't wait to get to know you better."
When Senpai said in the last panel "It's fine, you should go" - that's actually a test from Lady Senpai. The key to passing her test in this instance, is to rub it in to her jealous lady colleagues. And nothing rubs it in more than a handsome-looking man telling other ladies (in this case his new female admirers) that Lady Senpai is the best (obvs) while she's standing next to you, and have the confidence to take the initiative in taking her to lunch - tell her that's what you're going to do, not merely ask her.
If she hesitates but sends the right body signals (e.g. looking down and feeling blushed, stroking her hair etc.), add a few encouraging words like "You know, haters' gonna hate. Let's have fun together", take her hand and go.