Cut the cabbage into wedges and shred it with a sharp chef's knife or mandoline. Or use a food processor with the shredding disc.

Peel the carrots and shred or cut them into thin matchsticks.

Combine the shredded cabbage and carrots in a large bowl; toss with the celery seeds.

In a bowl, combine the mayonnaise, sugar, vinegar, oil, celery salt, pepper, salt, and lemon juice; pour over the cabbage. Toss to blend ingredients. If desired, add a small amount of cream or half-and-half, to thin.

Cover and refrigerate until serving time.