Separate 2 coddled yolks and place in food processor, discard whites. Add whole coddled egg, Dijon mustard, sugar, salt, pepper and 1/8 cup of the lemon juice. Pulse mixture for one minute.
With motor running, slowly add oil just dribbling it in until all the oil has been mixed in.
Scrape sides, stir by hand and taste. Add more salt, pepper or sugar as needed. Add additional tablespoon of lemon juice if needed.
Store any remaining mayonnaise in refrigerator for up to 5-7 days. Bring back up to room temperature before serving for the best flavor.