YABU to make this a hill to die on. Co parenting requires cooperation and compromise, there will be different rules at each house and you can't control what your Ex does with your DD, or how he parents, just because you don't like it.
I coparent DD13 with ExDH and she spends every other week with him.
DDs school lunches, when she was at primary, were free at KS1 and 2 so the default was for her to have school lunches because it was free, less hassle and she was happy with them. Sometimes she wasn't keen on what was on the menu (she would eat it, it just wasn't her favourite) so ExDH would often send her in with a packed lunch on those days because she asked for them. When she was with me and asked for packed lunches on those days I just said no as I knew she would still eat the lunch at school. It didn't take long for DD to learn that when she was with me it was 100% school lunches and not to ask for packed lunches because I'd say no whereas with her dad it was whichever she asked for on the day.
Since school dinners were free and the kids just had to confirm every day whether they had a packed lunch or we're having school lunch I didn't let it bother me that ExDH sent her in with packed lunches as it didn't affect me.
Once she moved to KS3 and lunches had to be paid for I made sure that ExDH and I were in communication about lunches because we had to ensure her lunch account was kept topped up. In the end we agreed that we'd both put in 50/50 of the weekly lunch amount (iirc it was something like £3 a day so £15 a week so £7.50 each) and if one or other of us sent her in with a packed lunch then that days lunch money would roll over to the next week and we'd just adjust our paying in accordingly. So if ExDH sent her in with a packed lunch one day then £3 would roll over to the following week; I'd top up the account £7.50 and he'd top up £4.50 and she's still have the full £15 in her account.
It requires communication and coordination but we've co-parented successfully for 8 years now by not falling out over petty things like one of us letting her have the odd packed lunch now and again.