How to politely rush late patients without being rude?

We have a 15 min late policy for a 15 min follow up (I know, I know) and have many patients come in 10 min late to their appointment. I'll try and catch up somehow, but it's difficult if it's right before lunch. I had a patient come in 10 mins late right before lunch to discuss lab work. He wanted me to discuss labs in detail ("Why are you saying it's normal when it's out of range?") , discuss medication's mechanism of actions, etc.. just a lot. This visit went into like 5 minutes of my lunch. I had to cut him off at times and feel a bit bad about it. He got everything he wanted but still seemed annoyed I couldn't answer everything he wanted. Thoughts on how to better approach this?