In a small bowl, stir together the mustard, capers, tarragon (if using), 2 tablespoons of the oil, and 2 tablespoons water. (If necessary, adjust the consistency with more water until the sauce is spoonable.)
Heat 1 teaspoon of the remaining oil in a large nonstick skillet over medium-high heat. Season the cod with ½ teaspoon salt and ¼ teaspoon pepper and cook until opaque throughout, 4 to 7 minutes per side.
Meanwhile, in a large bowl, toss the lettuce, cucumber, and onion with the lemon juice, the remaining 2 tablespoons of oil, and ¼ teaspoon each salt and pepper. Drizzle the cod with the mustard-caper sauce and serve with the salad.