Preheat barbecue to medium.
Coat chicken with 1 tbsp oil and 1/4 tsp salt in a medium bowl. Season with fresh pepper. Toss potatoes in remaining oil and salt in another bowl. Season with fresh pepper. Stir Dijon with honey and 1 tbsp thyme
Oil grill. Barbecue chicken and potatoes, with lid closed, flipping chicken halfway through, until chicken is springy when pressed, about 30 min. Transfer potatoes to a platter when they are fork-tender, about 15 min.
Transfer chicken to a platter with potatoes and brush with Dijon mixture. Sprinkle with remaining thyme.
Barbecue lemons about 1 min. Serve with chicken and potatoes.
