Bring 1” water to a boil in a large saucepan with a steamer basket inside. Use tongs to lower eggs into steamer basket, cover, and steam for 10 minutes. Fill a bowl with ice water and transfer eggs to ice water to cool. Crack eggs all over and peel, then slice crosswise.
Add green beans to steamer basket and cook until crisp-tender, about 3 minutes. Transfer to bowl of ice water with a slotted spoon and let cool completely.
In a medium bowl, stir together tuna, onion, and olives.
In a small jar, combine lemon juice, olive oil, salt, and pepper. Shake jar vigorously to combine.
Lay wraps on a countertop. Divide spring mix between them, top with tuna, eggs, green beans, and cherry tomatoes. Pour dressing over, roll up, and serve.