Vegetarian

They serve a lot of vegetables as soups.

Your diet sounds more like a vegan diet rather than vegetarian. Good luck. My daughter is vegan and she really struggled finding food when we were walking the Camino through Portugal.

Stick with pasta dishes, with tomato sauces, potatoes, rice, salads. Some places will just make you a platter of vegetables if you ask.

Most restaurants will have vegetarian dishes. I’m not so certain about vegan. But, if you do a search on vegan restaurants Lisbon, a number of places come up. Avoiding fats and oils may be your biggest challenge.

do you mean no animal oils or none at all? I haven't been yet - going in May - but I'm assuming olive oil is the most prevalent, as it is in Spain, Italy and Greece.

Don't go to Portugal.
The national foods are pork, pork, sardines, sardines.
And, potatoes.

Are you familiar with Happy Cow? https://www.happycow.net/

If you tell us more specifically what you can eat or not eat, it would be helpful. Is it no oils, or just animal based fats like butter or lard? If it is a vegan diet, then we can make more recommendations. What videos are you watching? Do you eat eggs? Any dairy products?
I am sure if you look on Trip Advisor for restaurants in Lisbon, you can use their filter to find vegetarian or vegan restaurants. This is not difficult to do.

Pretty much I eat vegetables, fruit, pasta, potato, no Meat, or no oil, no milk or cheese. when i went to Italy I couldn't tolerate their food.
Some flexibility with the diet is ok at times. Its not a strict diet. The video of the salted fish on the racks looked unappetizing.