Scrub baby potatoes and boil potatoes in lightly salted water for about 12 to 15 minutes until tender. Drain and peel when cool enough to handle. Cut into bite size pieces.
Boil eggs for 6 minutes. Remove and plunge into cold water. Peel and cut into halves.
Blanch green beans for 1 to 2 minutes. Transfer to cold water bath. Drain well.
Squeeze the 2 lemons to get about ⅓cup/160ml lemon juice into a jar with a lid.
Add all other lemon vinaigrette ingredients. Place the lid on and shake to combine.
Arrange lettuce leaves in a single layer on a large platter. Place tuna in the center surrounded by marinated artichoke hearts and pitted olives.
Arrange prepared baby potatoes, eggs, green beans, tomato wedges, cucumber, sweet peppers, onion around marinated ingredients on the platter.
Grind pepper all over ingredients over the platter. Arrange strips of anchovies (if using) over vegetables.
Just before serving, pour lemon vinaigrette all over salad.