In a large sauce pan, add enough salted water to cover the potatoes by 1 inch. Bring to a boil; lower the heat to medium-high and cook until fork-tender, about 15 minutes; drain. Let cool slightly, then slice.
Meanwhile, in a medium bowl, whisk together two-thirds of the lemon juice, the lemon zest, mustard and 2 tbsp. EVOO. Add the tuna, celery and onion and toss to coat. Season with salt and pepper.
In a large bowl, toss the arugula with the remaining lemon juice and 2 tbsp. EVOO; season with salt and pepper. Divide the salad greens among 4 plates, place a tomato on top of each portion and, using an ice cream scoop, stuff the tomatoes with the tuna salad. Arrange the potatoes around the base of each tomato.