For the pesto, combine the walnuts, Parmesan cheese, rosemary, olive oil, lemon zest, salt & pepper in a food processor. Pulse just until the mixture forms a paste, leaving the walnuts slightly coarse. Set aside.
Melt the butter in a medium cast-iron skillet over medium heat. Add the bread cubes and season with salt and pepper to taste. Turn the cubes and shake the pan frequently until lightly browned and crisp, about 3 minutes. Set aside.
Bring the broth to a boil in a pan just large enough to hold the chicken in a single layer. Add the chicken, lower the heat so the broth is at a slow simmer, cover, and poach until the chicken is just cooked through, about 15 minutes. Remove the chicken from the broth and cut on the diagonal into 1/4-inch slices. Season lightly with salt and pepper, return it to the broth, and keep it warm.
To make the salad, toss the asparagus tips with 3 teaspoons of the lemon juice and the salt and pepper. Set aside. Toss together the radicchio, arugula, the remaining 3 teaspoons lemon juice, the olive oil, and more salt and pepper to taste.
To assemble, place a dollop of the pesto in the center of each of 8 large plates. Alternate the asparagus tips and slices of the chicken over the pesto. Surround with the greens, top the greens with the croutons, and serve immediately.