Barcelona & Lisbon recommendations for mixed vegetarian/omnivore couple?

Excited to be heading for our first visits to Barcelona, and then to Lisbon with my omnivore husband. I’m a vegetarian who does eat food including milk and eggs (lacto-ovo). I’d greatly appreciate recommendations of humble and moderately priced restaurants in both areas, especially those specializing in local/regional foods.
We may do a bigger splurge once or twice in each place.

I’ve found great resources for the meals we’ll do in vegetarian restaurants, but the most wonderful meal experiences for us are often in omnivore restaurants that offer good options for vegetarians also. When we travel, those feel more like participating in the local culture.

Thanks in advance for any and all help!