Drain the tuna can well. Cut the half cucumber and half avocado into equal cubes. Squeeze the juice from the lemon.
Bring a pan of water to a boil and hard boil the two eggs for about eight minutes. Immediately chill the eggs under cold running water, peel off the shells and halve them.
Place the drained tuna in a mixing bowl and add the cucumber and avocado cubes. In a separate bowl, whisk together a dressing of the two tablespoons of olive oil, the lemon juice, salt and pepper. Pour this dressing over the tuna mixture and toss everything together well.
Distribute the lettuce over the plates to create a base. Spoon the prepared tuna mixture onto this bed of lettuce. Lay the halved eggs on the dish and serve immediately.