Finely grate the zest of 1 medium lemon (about 2 packed teaspoons) into a small jar or bowl. Juice the lemon (about 3 tablespoons) into the bowl. Finely chop 2 garlic cloves (if using anchovy fillets, finely chop 4 together with the garlic), chopping until it is paste-like. Add the garlic and anchovy or 2 teaspoons anchovy paste to the bowl.
Add ⅓ cup neutral oil, ¼ cup olive oil, 1 teaspoon Dijon mustard, ½ teaspoon kosher salt, and a few grinds of black pepper if desired. Whisk or seal and and shake the jar until combined and emulsified.