Place the cabbage, apples, and carrots in a large bowl. Mix in the dried cranberries and raisins.
In a small bowl, whisk together the lemon juice, apple cider vinegar, olive oil, honey, salt, and pepper until smooth.
Pour the dressing over the vegetable mix and toss until the slaw is evenly coated. Chill for at least 15 minutes before serving to let the flavors meld.