Halve avocado lengthwise, and remove the pit. Scoop out 2 tablespoons avocado flesh from each half, and leave the shells with the remaining flesh intact.
Mash the 4 tablespoons avocado with lemon juice and olive oil until smooth. Toss with tuna, sunflower seeds, half the lemon zest, and salt and pepper to taste. Fill halves with tuna mixture, and garnish with remaining lemon zest and basil, if desired. Serve immediately with a spoon.