In a stainless steel bowl, combine the lemon zest, lemon juice, sugar and salt. Whisk with a wire whip. Slowly whisk in the olive oil. Whisk in pepper and adjust the salt. Allow to stand 5 minutes before using.
Then, toss together 1/3 cup lemon vinaigrette, mint, red cabbage and carrots in a stainless steel bowl. Refrigerate for 10-20 minutes before serving.