Add the aquafaba, vinegar, salt, sugar, lemon juice, and mustard to a measuring cup.
Mix with an immersion blender until combined.
With the blender still running, SLOWLY pour in the oil. Adding all of the avocado oil should take about 5 minutes. Blend until you reach the desired mayo consistency.
Notes
Add your oil VERY SLOWLY to get the perfect thick and creamy consistency on your vegan mayo. Be patient, and don't lose hope during the first 2 to 3 minutes of blending because it will eventually thicken.
If your vegan mayonnaise doesn't thicken, put it in the fridge for at least 3 hours before use. The mayo will thicken as it sits in the fridge.