Combine the tuna, cilantro, ginger, jalapeno if using, shallot, soy sauce and sesame oil in a bowl; toss gently. Cover and refrigerate for at least 1 hour or up to 2 hours.
Just before serving, fold in the avocado. Scoop 1 1/2 to 2 tablespoons of the poke onto each on lettuce leaf. Serve.