I have worked in all the schools here. The elementary schools get 20 minutes to eat. 90% of the kids are done in 10. Those who are 't either have something to heat up, are slow(and some of those are slow on purpose) or are too busy talking.
I would make things as easy for him as possible. Have everything in bite size pieces. Everything in easy open containers or bags.
Yes 15 min is part of the problem, but the other half is your son is eating slow and needs to eat faster if he wants to finish everything.
Work with him in eating faster at home and use buying lunch as a reward.