In a medium saucepan, combine the eggs and enough water to cover. Bring to a boil, remove from the heat, cover and let stand for 12 minutes. Drain and let cool; peel and quarter lengthwise. Reserve the saucepan.
Meanwhile, bring a large saucepan of salted water to a boil. Add the green beans and cook until crisp-tender, about 3 minutes. Drain and rinse with cold water.
In the reserved saucepan, combine the potatoes and enough salted water to cover by 1 inch. Bring to a boil, then lower the heat and simmer until tender, about 20 minutes. Drain and let cool, then cut into bite-size pieces.
In a small bowl, whisk together the olive oil and lemon juice; season with salt and pepper.
Arrange the potatoes, green beans and tomatoes on a platter. Flake the tuna and mound over the vegetables. Top with the eggs. Drizzle the dressing on the salad.