Place them in a bowl filled with cold water and give them a quick wash, gently squeezing for a minute. Let them drain in a colander while preparing the brine.
In a bowl, combine ½ cup of white wine vinegar or apple cider vinegar, ¼ cup of lemon juice, ½ cup of room temperature water, 3 teaspoon of salt, and 2 teaspoon of sugar. Mix well until the salt and sugar are fully dissolved.
Place the shredded red cabbage in a clean glass jar, and pour the vinegar mixture over until the cabbage is fully submerged.
Seal the jar tightly and store it in the refrigerator for up to 3 weeks. Your pickled red cabbage is ready to it in only two hours.