Kansas City Steaks with Lobster Béarnaise Sauce

Name: Kansas City Steaks with Lobster Béarnaise Sauce
Ingredients: 1 2 1/3-pound live lobster; 1 cup (2 sticks) unsalted butter, divided; 1 shallot, sliced; 2 garlic cloves, chopped; 1 dried red chile, such as Japones or de árbol; 1 /2 teaspoon paprika; 1 /4 cup Sherry wine vinegar; 2 tablespoons chopped shallot; 1 tablespoon capers, chopped; 2 large egg yolks; 1 tablespoon fresh lemon juice; 1 tablespoon water; 1 tablespoon chopped fresh tarragon; 6 14-to 16-ounce 1 1/4-inch-thick New York strip steaks with bone, or 9-ounce boneless New York strip steaks; Coarse kosher salt