I haven't done European ports, but have done Bahamas with multiple severe food allergies.
I contacted
DCL's special services department (the same as I did to notify them about the allergies in the first place), explained the port excursions we were planning on taking, and asked if the included lunch could accommodate my allergies. DCL asked me to contact them closer to sailing (they gave a timeframe), but explained that when I did they would contact the excursion site, advise them about the allergies and confirm if they can accommodate. In both cases (Aquaventure, Blue Lagoon) the response came back that they could.
when we did the excursions and it came time for lunch, the site was in fact expecting me

Now, not the same comfort level I have with Disney for food, but I survived with no reactions
That said: I brought food with me just in case. Individually wrapped, so the extras could be brought back on board: Several Enjoy Life bars. A Capri Sun juice packet. A bottle of water.
When I was traveling on my own in Switzerland several years ago, I discovered that many of what we would think of as a "mom and pop" "convenience stores" (only nicer!) often carried a small amount of fresh products: fruit, veggies, breads, sandwiches. If your ports have similar little stores, while it isn not the most balanced of meals, its certainly enough to get one through a few hours until you're back on the ship. At the time I was not allergic to milk, so could do these really nice little ham and cheese on baguette sandwiches they had. there was one a short walk from my hotel and it became my go-to place for a quick meal (I ate a lot of those sandwiches).
Anyhow. your best option is to contact DCL special services and speak with them about your concerns and ask what they can do to help.
SW