In a bowl, mix the lemon juice, dark brown soft sugar, Dijon mustard, soy sauce, olive oil, garlic, ginger, salt and pepper. Place the lamb in a shallow container. Pour the lemon juice mixture over the lamb. Cover and marinate in the refrigerator 8 hours or overnight.
Preheat barbecue for medium heat. Drain marinade and bring to the boil in a small saucepan. Reduce heat to low and simmer, whisking constantly, until slightly thickened.
Lightly oil the barbecue cooking grate. Over indirect heat, grill the lamb 40 to 50 minutes, turning to cook all sides, to a minimum internal temperature of 63 degrees C. Cool, slice and cover with the thickened marinade mixture to serve.