Soak the red onion in cold water, 10 minutes. Meanwhile, cut the apple into matchsticks and toss with the lemon juice; set aside.
Toast the pecans in a medium dry skillet over medium heat, stirring occasionally, about 5 minutes. Transfer to a cutting board and let cool slightly, then roughly chop.
Toss the kohlrabies, 1 teaspoon salt and a few grinds of pepper in a large bowl. Combine the dressing and sugar in a small bowl. Drain the onion, squeezing out any excess water, then add to the kohlrabies along with the apple, carrots, parsley and toasted pecans. Add the dressing mixture and toss to combine; season with salt and pepper. Let sit 1 hour before serving.
Blue Cheese Dressing
Puree 1/2 cup each crumbled blue cheese and sour cream, 1/3 cup buttermilk, 1 small garlic clove (smashed) and 1 tablespoon white wine vinegar in a blender. Transfer to a bowl and stir in 1/4 cup more blue cheese, 2 to 3 dashes Worcestershire sauce and/or hot sauce, and 1 tablespoon chopped parsley. Season with salt and pepper. (Makes about 2 cups.)