Combine the mayonnaise, sour cream, lemon juice, pepper, salt, and half of the bleu cheese in food processor or blender.
Process until well combined.
Remove to storage container and stir in the remaining bleu cheese (or just mix all the ingredients in a container).
If too thick, stir in some alternative milk (like almond or coconut) to desired consistency.
Store tightly covered in the refrigerator 7 to 14 days.