Place the grated onion in a colander, rinse with cold water for about 1 minute, then drain thoroughly to reduce the sharpness
In a bowl, combine the avocado and mayonnaise, then mash together with a fork until well mixed
Add the drained onion, diced tomatoes, chopped parsley, lemon juice, and minced garlic to the avocado mixture and stir thoroughly
Season with sea salt to taste and adjust lemon juice if needed. The avocado mayonnaise can be prepared up to 6 hours ahead; cover it directly with cling film and refrigerate