Using a blender or immersion blender, combine tofu, lemon juice, and mustard. Blend until smooth.
With machine running, add oil in a very slow, thin stream (the slower and thinner the better - if not, you will find you mayo will start to separate as it sits in the fridge over time). Use enough oil until you get the thickness you want. Season to taste with salt.
Notes
Makes about 2 cups, and stores for about 10 days in fridge.