Fill a large pot with salted water and place over medium-high heat.
Add the octopuses and the potatoes and squeeze the juice of one lemon into water.
Bring the water to a boil and cook for 30-40 minutes, or just until the potatoes are cooked through; the potatoes and octopuses cook at the same rate.
Check for doneness by inserting a small, thin bladed knife into one potato.
Remove the pot from the heat and let the octopuses and potatoes cool in the water for about 30-40 minutes.
When cool, remove the potatoes from the water, cut them into 1/4 inch cubes and transfer into a large bowl.
Remove the octopuses from the water and cut them into 1/2 inch pieces.
Add the octopus pieces to the bowl with the potato. Add the olive oil and the juice from the other lemon to the bowl.
Toss and season with salt and pepper to taste. Top with parsley leaves.
Serve at once, from a large bowl or divided among salad plates.