Combine mustard, 1 tablespoon oil and pepper. Rub steaks with mixture. Cover and chill until ready to cook.
Place lentils, rosemary and stock in a pan. Bring to a boil, uncovered. Cover, cook lentils over low heat 20 minutes. Add carrots; cook another 10 minutes. Remove pan from heat. Leave lentils and carrots to cool in cooking liquid. Remove rosemary. Add 1⁄2 teaspoon salt.
Heat 1 tablespoon oil in a nonstick frying pan over medium–high heat. Add steaks; cook 3 to 5 minutes each side. Remove from pan, wrap in aluminium foil.
Whisk remaining 4 tablespoons oil and 2 tablespoons vinegar in a medium bowl. Add salt and pepper to taste. Drain lentils and carrots from pan and add to bowl. Stir in thyme. Whip cream in a small bowl until stiff; fold in the horseradish.
Slice steaks thinly and add any juices from meat to lentil mixture. Add remaining 1 tablespoon vinegar and salt and pepper to taste. Place lentil mixture on serving plates with lettuce. Add meat, top with a little horseradish cream mixture and sprinkle with chives. Serve remaining horseradish cream mixture separately.