In a large serving bowl, combine the chopped lettuce, radicchio, onion, celery, cherry tomatoes, peppers, sun-dried tomatoes, and chickpeas. Toss the ingredients together and set aside.
To prepare the dressing, combine all of the ingredients in a liquid measuring cup. Whisk until blended. Taste, and add more salt if desired.
If you’ll be serving all of the salad at once, go ahead and drizzle enough dressing in to lightly coat the salad and toss to combine. I prefer to store the salad and dressing separately so I can enjoy salad for a few days. Just whisk the dressing again before drizzling (if the olive oil solidifies a bit in the refrigerator, don’t worry, that’s normal—just let it warm up for about 5 minutes at room temperature or microwave for 10 to 20 seconds).