In a jar slightly larger than the head of your stick blender, put the garlic, lemon juice, and salt. Blend until very fine.
Add avocado and blend again until a smooth paste forms.
With the blender running, add the avocado oil and mix with blender head to create a stable emulsion.
Dice the chicken breast and place in a large bowl with celery and onion. Cover with avocado mayo, and season to taste with salt and pepper.
Assemble each sandwich with a slice of sourdough, a piece of lettuce, a generous portion of chicken salad, and the second piece of bread.