Whisk the balsamic vinegar, lemon juice and olive oil in a bowl. Taste for seasoning; add salt and pepper. Set aside.
Cut the cherry tomatoes in half and slice the beefsteak tomatoes. Arrange in a single layer; season with salt and pepper and sprinkle with the sugar. Transfer to a bowl and drizzle with half of the dressing. Add the tarragon and strawberries; toss.
Divide the tomato mixture among plates. Drizzle with more dressing and top with the watermelon. Serve immediately.
Alex uses cold watermelon and room-temperature tomatoes for this dish. "The contrast of temperatures gives the salad an extra-fresh taste."