Bring a sauce pan of water to a boil. Boil corn and edamame for 3 minutes.Remove from hot water with a slotted spoon, submerge immediately in ice water.Drain and place in a large bowl. Add tomatoes and avocados.In a small bowl, add lime juice, salt, pepper and gradually add oil whisking as you add oil.Pour over salad ingredients and toss to coat.Arrange lettuce leaves on a platter.Spoon salad mixture onto lettuce leaves.Garnish with cilantro.