Step 1Place the celery, onion, lemons, parsley sprigs, wine, white wine vinegar and 1 tablespoon salt in a 6-quart stock pot. Fill it with water and bring it to a boil.
Step 2Wash the octopus in cold running water and (if not done already) with a paring knife remove the beak, which is where the tentacles meet in the center of the octopus, by cutting a circle around it. Place the octopus in boiling water, reduce the heat and simmer, covered, until tender, about 2 hours for a 2 1/2 - to 3-pound octopus. Boil the potatoes in a separate pot of salted water until tender, 20 minutes. Peel and slice diagonally into one-third-inch-thick pieces.
Step 3Carefully remove the octopus from the water. Cool slightly. Cut the tentacles into one-third-inch pieces. Gently mix the octopus, potatoes, chopped parsley, olive oil, lemon juice, red wine vinegar and salt and pepper to taste. Serve warm or at room temperature.