Preheat a grill to medium and position a large cast-iron skillet off to the side. On an 18-inch sheet of heavy-duty foil, toss the wet potatoes with 1 tablespoon olive oil; season with salt and pepper. Arrange the potatoes in a single layer and wrap tightly to enclose. On a 12-inch sheet of foil, toss the wet green beans with 1 tablespoon olive oil and season with salt and pepper; wrap tightly to enclose. Brush the scallions with 1 tablespoon olive oil, season with salt and pepper and set aside.
Place the packets of potatoes and green beans on the cooking grate; arrange the bacon in a single layer in the skillet. Cover and grill, turning the bacon once, until crisp, about 7 minutes. Remove the green beans from the grill and open the packet to let them cool. Carefully remove the skillet from the grill and drain the bacon on paper towels, reserving the fat. Arrange the scallions on the cooking grate and grill with the potato packet, turning the scallions occasionally, until they are just charred, about 5 minutes, and the potatoes are fork-tender, about 15 minutes. Open the packet to cool the potatoes.
In a large salad bowl, whisk together the lemon juice, mustard, reserved bacon fat and the remaining 3 tablespoons olive oil. Quarter the potatoes, halve the green beans and coarsely chop the scallions; add to the bowl along with the tuna and spinach. Season with salt and pepper and toss. Crumble the bacon on top before serving.