Prepare beans:
Coarsely mash about half the beans with a fork in a bowl, then stir in remaining beans, garlic, 1-tablespoon lemon juice, 2-tablespoons oil, 2-tablespoons parsley, and 1/4 teaspoon each salt, and pepper.
Make tuna:
Flake tuna in a bowl with a fork, then stir in 2-tablespoons basil, olives, celery, onion, 2 tablespoons oil, 1-tablespoon lemon juice, and 1/4-teaspoon each salt and pepper until combined.
Gently combine bean and tuna mixtures and serve at once.