Prepare a charcoal or gas grill for high heat (450° to 550°; you can hold your hand 5 in. above cooking grate only 2 to 4 seconds). In a small bowl, combine horseradish, 2 tbsp. oil, and garlic. Spread half of mixture over one side of steak.
Using a wad of oiled paper towels and tongs, oil cooking grate. Lay steak, sauce side down, onto grate. Spread remaining sauce onto top side. Grill steak, turning once, until done the way you like, 10 minutes for medium-rare. Meanwhile, grill mushrooms next to steak until warm and grill marks appear, about 6 minutes. Transfer steak to a cutting board and sprinkle with sea salt. Tent with foil and let rest 10 minutes.
Put mushrooms in a medium bowl. Add mâche, remaining 2 tbsp. oil, lemon juice, kosher salt, and pepper, and gently toss to combine. Serve next to steak.
Note: Nutritional analysis is per serving.