Cook the eggs in boiling water for about 10 minutes. In the meantime, halve the chilli pepper, remove seeds and chop finely. Peel garlic and chop finely. Mix 3 tablespoons lime juice, garlic and chilli.
Season with salt and sugar. Whip the oil drop by drop. Drain the eggs, rinse with cold water, peel and quarter them lengthwise. Drain the tuna. Clean, wash and spin-dry lamb's lettuce.
Remove outer iceberg lettuce leaves and cut lettuce into slices. Wash, clean and slice the tomatoes. Cut avocado in half, remove stone. Halve halves again and remove flesh from skin.
Cut the avocado quarter into slices and sprinkle with 1 tablespoon lime juice. Peel onion and slice thinly. Mix tuna, lamb's lettuce, iceberg lettuce, eggs, tomatoes, avocado and onion.
Drizzle with the vinaigrette. Arrange salad on plates. Serve with baguette.