In a small bowl, combine the thyme, oil, ½ teaspoon salt, and ¼ teaspoon pepper. Rub the mixture over the steak.
Grill or broil the steak 4 to 5 minutes per side for medium.
Remove the steak and let sit, covered with foil, for 5 minutes before slicing.
Meanwhile, in a small bowl, combine the mayonnaise, tarragon, lemon juice, and ¼ teaspoon salt and mix well.
Layer the bread with lettuce and steak and drizzle with the mayonnaise mixture.