Preheat oven to 400 degrees.
In a large baking pan, arrange the potato pieces and cover with about 1/2-inch water.
Drizzle with half the olive oil and the juice of 1 lemon, tossing the lemon rinds into the pan alongside the potatoes.
Sprinkle to taste with sea salt, oregano, and pepper; place in oven for about 20 minutes.
Squeeze the second lemon over the potatoes, adding the rind, toss the potatoes around using a spatula, taking care not to break them up too much, and scatter the pieces of garlic around the pan.
Add more olive oil, if needed; return to oven.
Bake for another 15 minutes or so, remove from the oven, toss around a bit, then return for another 5 minutes.
Remove from the oven, squeeze the last lemon over the top, and scrape all the yummy pan juices up along with the potatoes.
Serve right away (though they are not bad at room temperature).