Make pickled onions: Put onion slices in a pint-size jar. In a liquid measuring cup, combine remaining pickled-onion ingredients, stir to mix, and pour over onion slices. Push slices down with a fork until submerged in the liquid. Seal jar and chill at least 30 minutes (4 hours is ideal) and up to 1 week.
Marinate fish: Whisk together 1/4 cup oil, the oregano, and lime zest in a bowl (it will be thick, like pesto). Pat fish dry with paper towels, then add to bowl and turn to coat thoroughly with marinade. Chill at least 30 minutes and up to 3 hours.
Make salsa: Put pineapple in blender, followed by remaining salsa ingredients, and blitz until smooth. Adjust seasoning with salt, pepper, or more lime juice to taste.
When you're ready to cook the fish, heat a grill to medium-high (450°) with a large cast-iron frying pan or griddle set on cooking grate. Meanwhile, toss fish with salt and pepper.
When pan is hot enough that it evaporates a drop of water instantly, swirl remaining 1 tbsp. oil into hot pan, add fish in a single layer, and cook undisturbed, grill covered, until browned underneath, 2 to 3 minutes. Carefully flip pieces over with a fish spatula or other thin spatula. Cook 2 to 3 minutes more, covered, or until fish is cooked through.
Arrange lettuce leaves on a platter (if any are torn, top with a second leaf). Arrange fish on lettuce, tearing pieces to fit, and season with salt if you like. Add sliced avocado, a drizzle of salsa, and pickled onions. Serve with lime wedges and remaining salsa on the side.
*Avoid cod; it's too soft and will flake apart here. Tam uses Diamond Crystal kosher salt, which has bigger crystals than Morton--so if you're using Morton, cut the amount by a third.
Make ahead: Pickled onions, up to 1 week, chilled; salsa, up to 4 days, chilled.