Place the canned tuna in a fine-mesh strainer over the sink and let it drain thoroughly.
Meanwhile, in a mixing bowl whisk together the mayonnaise, Dijon mustard, 1 tablespoon lemon juice, and celery seed; season with salt or Vege-Sal to taste.
Chop the green onions and, if using, halve or chop the cherry tomatoes and dice the avocado.
Toss the avocado with the remaining 1 tablespoon lemon juice to prevent browning, then stir in the chopped tomatoes and set aside.
Transfer the drained tuna to the mixing bowl (use a bowl with a lid if saving leftovers) and mix in the mayonnaise dressing until evenly coated.
Fold in the dill pickle relish, capers, and sliced green onions until combined.
Separate and rinse romaine leaves, spin or pat dry, and select 8 large leaves for serving.
Spoon about two generous tablespoons of the tuna mixture into each lettuce leaf, top with the tomato–avocado mixture if using, and serve immediately.