To make the dressing, combine the yogurt, lemon, coconut aminos, salt, pepper, garlic powder, and anchovies in a wide-mouth jar. Using an immersion blender, blend the dressing as you slowly stream in the olive oil. Blend until the dressing is creamy and fully emulsified. Set aside.
To prep the salad, combine the romaine, chicken, cucumber, salt and pepper in a large salad bowl. Add about half of the dressing and toss well, adding a touch more dressing if desired. Set aside.
Dip the rice paper in a large bowl of water for about 5 seconds, rotating to wet all of the paper. Transfer the rice paper to a large plate or clean workstation and allow to sit for a few seconds to soften further.
Add about 1/2 cup worth of salad to the center of the rice paper. Roll the rice rolls by folding in the two corners, then folding up the bottom edge and rolling into a tight roll. Set aside and repeat for all of the ingredients.
Serve the rice paper rolls with extra dressing on the side for dipping!