Cut about 2” off of the end of the asparagus.Place, upright, in a container of ice water for at least 30 minutes.Trim the chicken breasts.Place between 2 sheets of plastic wrap and pound with a veal pounder (or other smooth, heavy object such as a rolling pin) to about 1/4” thickness.
Whisk together the mayonnaise, honey, mustard, pepper sauce and salt until smooth.Stir in the tarragon.
Place the asparagus in a single layer in a shallow baking pan.With a pastry brush, coat each spear well with the mayonnaise mixture.Place on a hot grill or in a 400 º F. oven and roast for 15 to 20 minutes or until “crisp-tender” and lightly browned.Remove and cool.
Coat the chicken on both sides with the mixture, reserving the remainder of the dressing.
Grill or broil the chicken on high heat, turning once, for about 5 minutes on the first side and 2 to 3 minutes on the second side.Cut into strips.
Whisk the lemon juice in the remaining dressing.
Arrange crisp lettuce leaves on a platter (or individual plates).
Arrange the chicken strips and asparagus spears on top.Drizzle over desired amount of the dressing.Garnish with the green onions.