I'd tell the parents the night before your next pickup morning: "I'm doing pickup tomorrow morning and just wanted a word with you. Last week (or whenever), Billy brought breakfast with him and I let him eat it in the car then -- but I can't do that next time. I have a 'no eating in the car' rule for my own family and need to keep to that during the carpool. If Billy's running late and hasn't had breakfast, he can bring it to eat at school but please don't send it with the expectation he'd eat in the car."
I would not just wait and see if Billy brings breakfast and then tell him, "Sorry, you can't eat that." If you do that, Billy's going to tell mom and dad that night how the mean mom didn't let him eat, he was starving, he was so distracted by being hungry, etc. Don't let them hear it from their son, let them hear it from you before he ever gets in he car with food.
If Billy - or the parents -- complain that "Mom X and Dad Y in the carpool let kids eat in their cars" and so on, you'll need to paste on a big smile (even on the phone -- they can hear it in your tone....) and say, "I realize other drivers might have different rules, and that's fine but we really need to stick to our rule in our car."
The lateness is a total pain, I agree, but I'd keep it separate from the food issue. If the kid is just a few moments late, that's one thing and can be ignored, but if he's quite late and actually making you rush to get to school on time, then it's time for another talk with the parents. If his lateness is causing a rush and pushing the carpool up against the school bell, I would talk with other drivers in the carpool and see if they have the same issue with this family. It will be much more effective if a couple of the carpool drivers, together, tell this family that the lateness is a problem, than if you do it all by yourself.