Shred cabbage and carrots finely; combine in a large bowl and mix evenly.
In a small bowl, whisk together mayonnaise, vinegar, sugar, salt, and pepper until smooth.
Add optional lemon juice and/or onion powder or celery seed if desired.
Pour dressing over shredded cabbage and carrots.
Toss thoroughly to coat all vegetables evenly.
Taste and adjust seasoning with salt, pepper, or vinegar as needed.
Cover and refrigerate for at least 1 hour to let flavors meld.
Serve chilled as a side dish with chicken, sandwiches, fries, or burgers.