Mix the lemon juice, brown sugar, Dijon mustard, soy sauce, oil, garlic, ginger, salt, and pepper together in a medium bowl. Place lamb in a shallow container. Pour lemon juice mixture over lamb. Cover, and marinate in the refrigerator 8 hours or overnight.
Preheat an outdoor grill for medium heat. Transfer marinade to a small saucepan and bring to a boil. Reduce heat to low, and simmer, whisking constantly, until slightly thickened.
Lightly oil the grill grate. Over indirect heat, grill lamb, turning occasionally, until cooked to a minimum internal temperature of 145 degrees F (63 degrees C), 40 to 50 minutes. Cool slightly, slice, and serve with marinade.
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