If you're making the mayonnaise by hand, put the bowl on a damp towel to keep it from moving around while you work. Then drizzle in the oils, whisking constantly, to form an emulsion. If the mayonnaise breaks, stop drizzling and whisk until it comes together again. If you're using the food processor, pour in the oils in a thin stream, with the machine running. Taste and adjust seasoning with salt and pepper and more lemon juice.
Yield: 2 cups