Use a sharp knife or mandoline to finely shred the cabbage into thin, crisp strands, then transfer to a large mixing bowl.
Shred or julienne the carrots until they’re bright orange and crunchy, then add them to the bowl with the cabbage.
In a separate small bowl, whisk together the mayonnaise, lemon juice, vinegar, and sugar until smooth and slightly glossy.
Pour the dressing over the shredded vegetables, then toss everything together until the cabbage and carrots are evenly coated with a shiny, creamy layer.
Add salt and pepper to taste, then gently fold again to distribute the seasoning evenly.
Cover the bowl with plastic wrap and refrigerate for at least 30 minutes to allow flavors to meld and the crunch to stay fresh.
Once chilled, give the coleslaw a final toss, taste for seasoning, and serve cold with your favorite dishes.