Bring a large pot of salted water to a boil. Add the green beans and cook until crisp-tender, stirring occasionally, about 4 minutes. Using a mesh strainer, transfer the green beans to a large bowl of ice water to cool completely. Drain the green beans and pat dry with a towel. Return the water to a simmer, add the potatoes, and cook until they are just tender but still hold their shape, 8 to 10 minutes. Transfer the potatoes to the ice water to cool completely. Drain the potatoes and pat dry with a towel. Bring the water back to a boil and add the pasta. Cook until tender, stirring occasionally, 10 to 12 minutes. Drain and set aside.
In a small bowl, whisk together the lemon juice, garlic, olive oil, oregano, salt, and pepper. Place the tomatoes, basil, and parsley in a large serving bowl. Add the tuna and toss gently to combine. Add the green beans, potatoes, and pasta. Pour the dressing over the salad and toss again to coat the salad with the dressing.
