.Bring a pot of salted water to a boil and add the green beans. When the water comes back to a boil, take the green beans out and add to a bowl of ice water. Once they are cooled, drain them, pat dry and chop.
Combine the mayo, olives and lemon juice in a food processor and process until just about smooth. Transfer this mixture to a bowl.
Drain the tuna and stir it into the mayo mixture. Add the eggs, tomatoes, green beans, dill, and the salt and pepper (to taste) and mix together.
Toast the bread slices. Divide the tuna onto 4 slices of the bread, top with lettuce and remaining bread slices.