In a medium bowl, pour roughly 2 tablespoons of the lime juice over the cubed avocado. Sprinkle a pinch of salt and pepper over the avocado too. Gently mix everything together. Set aside.
In another bowl, add the cooked chicken, green onion, and celery.
Gently stir in the mayo, starting with 1-2 tablespoons, in with the chicken mixture. You'll be able to add the last tablespoon of mayo later, if you think you need it.
Throw in cilantro and the avocado mixture. Again, gently mix everything together.
Taste your salad...now it's time to add ¼ teaspoon of salt, lime juice, dried dill, pepper, and the remaining mayo. Add your seasonings (and mayo) in small increments and taste as you go.
Keeping adding more seasonings until you get the taste how you like it, you may find additional salt, lime, and mayo is not needed.
Once you like the taste, toss in your tomatoes, stir, serve, and enjoy!