Wrap the potatoes individually in foil and bake for 45 mins - 1 hour until cooked through. Cool in the fridge or freezer until you can handle them, or do this in advance and leave them in the fridge overnight. Cut the potatoes into chunks, and toss with 3 tablespoons of dressing. Stir occasionally to help all the dressing absorb.
For the beans, blanch in boiling salted water for 1 minute, then drain and let cool.
Combine the tuna, lemon juice, dill, pepper, and olive oil.
To assemble, arrange the lettuce on a large platter. Top with the potatoes, green beans, tuna, and sprinkle with capers.
Serve with pickles and extra dressing, for drizzling.