Rinse and drain the beans. Drain tuna and olives. Cut the tuna into pieces. Peel and halve the onion, cut into slices and fry in 2 tablespoons of hot oil over medium heat until golden brown.
Wash, clean and slice the tomatoes. Arrange the tomatoes on 4 plates. Wash the thyme and dab dry. Remove the leaves from half of the thyme twigs. Mix lemon juice, 2-3 tablespoons water, salt, pepper and thyme leaves.
Fold in the remaining oil. Swirl the beans and olives in the salad dressing and arrange on the plates with the onion wedges. Add the tuna. Garnish with remaining thyme and possibly basil.