Put Dr Pepper, soy sauce, lemon juice, peppercorns, salt, and garlic in a gallon zip-loc bag. Seal the beef in the bag. Refrigerate for at least 5 hours or overnight.
Preheat a grill to medium. Place the tenderloin on the grill, reserving the marinade, and cover the grill. Cook, turning occasionally, until the meat registers 125 degrees F on a meat thermometer for medium rare, about 40 minutes. Transfer to a board to rest for 15 minutes.
Meanwhile, bring the reserved marinade to a boil in a medium saucepan, then lower the heat and simmer until slightly reduced, about 10 minutes. Slice the beef and drizzle with the Dr Pepper sauce.