He's a grown up and he works with other people. It is embarrassing for a guy to say "Sorry, my wife says I can't go out with you today". That's just humiliating. You are not his mother so stop telling him what he can and cannot do. It makes you look like a nag and you don't want to be that, you want to be his concerned wife who wants to have some extra money for other stuff.
Don't you ever think about how your co-workers perceive you? Don't you think they feel sorry for you for having to take your lunch every day? that you don't make enough money to join them for lunch? Do you think of you when there is a promotion or special project? No they think of the people they spend their lunch and break time with.
Give him an allowance out of the income and it is for his personal use, he does not have to report anything to you of how he spends it. It should be enough to cover his food costs and a few other things, a percent of his income. This money is not in any way accountable to you or anyone else. He can blow it on bubble gum every day if he wants to. It is his to spend. If he spends all his money on a few days lunches then he does without.
But if the guys in the office go out together every day you are going to have to make some other adjustments. He is doing networking and other possible connections during this time. It is not always about sitting around goofing off at lunch. They say that more business deals are made on the golf course that anywhere else, that can also happen at lunch, and other venues. It may be a needed socialization time for his job. You may have to accept it.
I think if you give him a credit card that is in his name only and he is responsible for making all the payments and if he doesn't then he loses it this gets it totally off your radar too.
Having a time set aside to work on the budget and setting aside the money he needs for this should be about working together, no one is the boss of anyone else. It should go something like this.
"Honey, I'm concerned about the amount of money we are showing charged on the credit cards. I don't know how we are going to be able to pay this bill every month. Do you have some ideas of how to cut our spending?"
He should be willing to work on the budget more since you asked for his help in making a better budget and plan.
He may also have different priorities. I value having groceries in the pantry and having a stock of several months of dry good in the pantry so if we have an unexpected bill there is enough food for me to feel safe.
My hubby would rather put money aside to go on vacation to someplace wonderful, I can't imagine paying a hundred dollars per night for hotel if we don't have, in my opinion, enough groceries. So we do without saving any money for vacation. We haven't been anywhere in years. We have different ideals about where our money should be going. I win though.
You need to try to work through this because this is definitely something you should be able to come to some kind of agreement on.