To make the dressing: In the bowl of a food processor or mini chopper, add the walnuts, shallots and garlic. Pulse until the walnuts are crumbly but the mixture is starting to get a little pasty. Add the oil, vinegar, honey, salt and pepper and puree until smooth. Adjust the seasoning if necessary.
For the salad: Bring a large pot of salted water to a boil. Fill a large bowl with cold water and ice and set aside. Cook the asparagus until crisp-tender, 1 to 2 minutes, then transfer immediately to the ice bath to chill for 2 to 3 minutes. Drain and pat dry. Cut diagonally on a long, sharp bias into 2-inch pieces. Add to a serving bowl.
Add the radishes to the asparagus. Squeeze the lemon juice over the vegetables and season with a pinch of salt and a few grinds of pepper. Gently toss. Spoon the dressing over the salad and toss again. Arrange the avocado over the salad, then garnish with the tarragon and serve immediately.