There are many recipes for home made mayo on the internet, youtube and PInterest.
Basically all mayo is, is oil, vinegar, egg, a pinch of salt, pinch of sugar, a dab of mustard, and maybe some herbs or flavourings.
So you can convert ANY may recipe to Low Carb by subtracting the sugar, and replacing it (if you want) with a sugar substitute.
Don't mess with the mustard quantities though. Mustard does contain a few carbs, but you will be only eating minute amounts in the final mayo, and you need it for the emulsification, so that the oil and vinegar don't separate out.