Start by shredding the cabbage and carrots.
Use a sharp knife or a food processor for evenly sized pieces.
In a large mixing bowl, combine the mayonnaise, sugar, apple cider vinegar, and lemon juice.
Whisk these ingredients until smooth and creamy.
Gradually add the shredded cabbage and carrots to the bowl.
Mix everything thoroughly until the vegetables are evenly coated with the dressing.
Sprinkle in the salt and black pepper.
Mix again to incorporate the seasoning into the coleslaw.
Cover the bowl with a lid or plastic wrap.
Refrigerate for at least one hour to let the flavors meld together.