In a food processor fitted with the slicing blade, thinly slice the cabbage.
Switch to the shredding blade, and shred the beet and apples.
In a large bowl, whisk the vinegar, lemon, sugar and salt, then whisk in the oil.
Add the shredded vegetables to the bowl and toss to mix. Add parsley and serve,or transfer to a storage tub and refrigerate for up to 4 days.