Cook the potatoes in boiling salted water for 15 minutes, or until tender. Drain, and cut in cubes and place in a bowl. Drizzle with the olive oil and toss well. Cook the string beans in boiling salted water for 3 minutes, then drain and refresh under cold water. Drain well and keep aside.
To make the vinaigrette, whisk together the garlic, mustard, vinegar and lemon juice. Add the oil in a thin steady stream, whisking until smooth.
Put the tuna in a bowl and separate into large chunks with a fork. Cover the bottom of a serving dish with the lettuce leaves. Scatter the potatoes, beans, tuna, tomatoes, olive and capers over the leaves pour the vinaigrette over the top and decorate with the eggs and anchovies.