Remove roast from refrigerator 30 minutes before cooking. Preheat oven to 400 degrees. Using kitchen twine, tie beef at 1 1/2-inch intervals; pat dry with paper towels. Season with salt and pepper.
In a large pan, heat 2 tablespoons oil on high. Brown roast all over, 9 minutes. Place on a rimmed baking sheet; sprinkle with thyme. Reserve half of one celery root for roast beef sandwiches; cut remainder into 1 1/2-inch chunks. In a bowl, toss celery root and potatoes with 2 tablespoons oil. Season with salt and pepper; add to sheet. Roast until beef is medium-rare, about 40 minutes (an instant-read thermometer inserted in center should register 125 degrees). Transfer beef to a cutting board; tent with foil. Let rest 15 minutes.
Meanwhile, whisk together lemon juice, vinegar, and 2 tablespoons oil; season dressing with salt and pepper. Save a handful of watercress for sandwiches; toss remainder with dressing. Reserve one-third the beef for sandwiches; slice remainder. Serve beef and vegetables with salad.
For tomorrow's sandwiches, refrigerate reserved watercress, celery root, and roast beef. To keep watercress crisp, wrap it in paper towels.