1. Combine the octopus, bay leaf, thyme, peppercorns, 1 teaspoon salt, the garlic, and 1 of the lemons, cut in half, in a saucepan along with water to cover. Turn the heat to medium, cover, and bring to a boil. Adjust the heat so that the liquid simmers slowly and cook until the octopus is tender, 30 to 90 minutes (check with the point of a sharp knife). Drain, discarding all the solids (except for the octopus). You can prepare this 24 hours in advance up to this point; cover and refrigerate the octopus.
2. Start a charcoal or wood fire or preheat a gas grill; the fire should be quite hot and the grill rack about 4 inches from the heat source. Cut the octopus into large serving pieces, brush it with half the olive oil, and sprinkle it with salt and pepper. Grill it quickly, so that the outside browns before the inside dries out. Cut the remaining lemon into wedges.
3. Brush the octopus with the remaining olive oil. Serve with lemon wedges, hot or at room temperature, garnished with the parsley.