Preheat oven to 425° F. For each packet, cut a large piece of parchment paper into a 16-inch diameter heart by folding each piece in half and using scissors to cut half a heart. Unfold and set aside.
In medium bowl, toss together the potato slices with a tablespoon of olive oil, the oregano leaves, and a couple pinches of salt.
Open the parchment hearts and just off-center, arrange a thin layer of slightly overlapping potato slices to make a base for one piece of fish.
Place a piece of fish on top of the potato slices, top with: two slices of lemon, a few olives, a pinch or two of sea salt, and a drizzle of olive oil. Sprinkle on any remaining oregano leaves from the potato bowl.
Seal the packages:
Wash and dry your hands so that you can seal the hearts clean and tight with little folds. Start at the rounded top of the heart and fold over the edge twice and crimp with your fingernail against work surface. Move down and make another fold about every 1–1½ inches, each double-fold overlapping the last, all the way around the edge of each heart and finish by twisting the end at the point.
Place packets on a rimmed sheet pan. Bake for 20 minutes or until packets are slightly brown and puffed. Remove from oven and let stand 5 minutes. Serve packages directly on plates so each person can cut theirs open at the table.