In a large nonstick pan, heat 1 tablespoon of olive oil over medium heat, add potato and saute until brown on the outside, soft on the inside, about 35 minutes. Stir occasionally. Place in a large bowl.
Using the same pan, heat another 1 tablespoon of oil, add cherry tomatoes and saute, stirring constantly, 2 minutes.
Stir in corn and tarragon, cook for 2 minutes. Place in bowl with potatoes.
In a cup, mix the lemon juice, salt, pepper, and remaining 2 tablespoons of oil, poor over potato/tomato mixture, mix well.