In a small bowl, whisk together the zest and juice from the lemon and the lime. Whisk in the soy sauce, sesame oil, and grated ginger, and season with the black pepper.
In a separate bowl combine the avocado, chopped shallot, and season with a dash of lime juice. Mash lightly with a fork and set aside.
Place the tuna steak in a plastic bag and pour the marinade over. Seal the bag and let it stand at room temperature for at least 15 minutes.
Heat the vegetable oil in a large skillet on MED-HIGH. Pat dry the tuna steaks with paper towels and place them in the hot skillet. Sear for 1 minute, then carefully flip over.