Make your own, it's easy. 1/2 cup oil of your choice, dash of dry mustard, 1 egg, tsp of lemon juice.
Blend egg with mustard & lemon in blender or with wand mixer. Slowly (and I do mean SLOWLY!) drizzle in the oil. Mixture will thicken as oil emulsifies. When all the oil is incorporated, you may add additional spices if you wish, but by hand, don't use the blender/mixer (try garlic and parsley or cilantro)

Using 1/2 cup of oil means that 1/4 cup of the resulting mayo will be the equivalent of 2 TBSP of oil. Adjust your intake accordingly to follow your plan's rules on fat.