In a small food processor, combine the anchovies, garlic, lemon juice, mayonnaise, mustard, and salt. Pulse until smooth. Stream in the oil slowly, pulsing to combine. If you don’t have a food processor, mince the anchovies and garlic by hand and whisk into the remaining ingredients. Taste for seasoning, and add more salt or lemon juice, as needed. Refrigerate in an airtight container for up to 1 week.