Tear the lettuce into approximately 1-inch pieces and place in a large bowl. Cut the mushrooms, fennel and radishes into 1/8-inch-thick slices using a knife or a mandoline. Add to the bowl with the lettuce.
Whisk the oil, lemon juice, chives, lemon zest, salt and pepper in a small bowl to blend. Add the dressing to the salad and toss to blend.
Divide the salad among 4 plates and serve.