In a large mouth mason jar, add the oil to the 1 cup mark, egg, and lemon juice.
If using an immersion blender, insert the wand in the mason jar, blend the liquid while moving the blender up and down to emulsify the oil.
If you are using a blender, add the egg and lemon juice to the blender first. Drizzle the oil into the blender slowly as the blender emulsifies and the oil thickens.
If making an egg-free AIP-friendly version, blend soaked raw cashews or macadamia nuts in a high power blender (like Blendtec or Vitamix) first, and then, drizzle the oil and lemon juice.
Add the mustard and sea salt. Blend to incorporate for a few seconds.
The mayo will thicken as you blend. Make sure to incorporate all the oil as you move the immersion blender wand up and down.
When done, close the lid and store in the refrigerator for up to 4 weeks. If using a blender, scrape every drop of the mayo into an airtight container, refrigerate up to 4 weeks. (This reason alone is worth investing in an immersion blender.)
Since you will be using raw eggs, it's really important to use farm fresh eggs that are from free roaming chickens that were pastured raised.
For egg-free version - use soaked raw cashews. Blend the cashews in a blender, and add to the mayo at the end and use the immersion blender to mix.
For AIP friendly version - use equal amount of pam shortening as the oil used.