Cut the ripe avocado in half, remove the pit, and scoop the flesh into a medium-sized mixing bowl. Use a fork or a potato masher to mash the avocado until smooth and creamy.
Pour 2 tablespoons of lemon juice into the mashed avocado and stir thoroughly to combine. The lemon juice adds a touch of acidity and helps to keep the avocado mayo fresh.
Open and drain the tuna cans, making sure to remove excess liquid. Add the drained tuna to the avocado mixture. Gently fold the tuna into the avocado mayo until the tuna is evenly coated and well combined, being careful not to break up the tuna too much.
Dice the cucumber and celery into small, uniform pieces. Add these diced vegetables to the tuna and avocado mixture. Gently mix to distribute the vegetables evenly throughout the salad.
Finely chop the fresh dill and chives. Stir the chopped herbs into the tuna salad mixture. The dill and chives will add a burst of fresh, herbaceous flavor.
Taste the salad and season with salt as needed. Adjust the seasoning according to your preference.
Transfer the tuna salad to a serving bowl or individual plates. Garnish with freshly chopped parsley for an added touch of color and flavor. Serve immediately or chill in the refrigerator until ready to serve.