Cover the dish with foil, place the baking dish on a baking sheet (it's likely to boil over a bit while in the oven and this will save you from a big oven cleaning), and transfer it to the oven. Bake the dish until the potatoes feel tender when a paring knife is inserted into the center of the dish, about 45 minutes. Remove the foil from the pan and let it keep baking to brown the cheese on top, about 15 minutes. Remove from the oven and let the potatoes rest 5-10 minutes before serving.
While the potatoes are cooking, in a small sauce pan over medium-high heat, bring the apple juice, brown sugar, thyme, cracked garlic cloves and lemon slices up to a bubble. Continue to simmer until it has reduced to about 3/4 of a cup.
While the apple juice is cooking, season the chicken pieces with some salt and pepper and drizzle with a little EVOO. Transfer the chicken to a baking dish and pour the reduced apple juice over all the chicken. Transfer to the oven and roast for 35-40 minutes, until brown and a thermometer reads 165ºF. Serve the chicken with a scoop of the potatoes alongside.