1. Make the carrots: Combine the julienned carrots with salt and acid. Refrigerate for 10 minutes or until ready to serve (or up to a week in advance).
2. Combine all horseradish aioli ingredients and whisk well until combined. Refrigerate until ready to serve (or up to a week in advance).
3. Prepare the steak: Heat two tablespoons oil in a large skillet over medium heat. Add the onion and sauté until browning, about 20 minutes. Add the steak to the pan. Season with salt, then stir every few minutes until the meat is browned on all sides, about seven to 10 minutes.
4. Assemble tacos: Fill the lettuce with meat and carrots, and drizzle with dressing. Add a radish slice and some cilantro, if using. Serve immediately.