Preheat the oven to 350 degrees F (175 degrees C).

Melt butter with olive oil in a large Dutch oven over medium-high heat. Add chicken to the Dutch oven and brown on all sides in butter and oil, 5 to 10 minutes. Remove chicken to a cutting board.

Drain all but 2 tablespoons of liquid from the pot; stir garlic cloves into the reserved liquid. Return chicken to the pot; sprinkle water, lemon juice, salt, thyme, and black pepper over the chicken; cover tightly.

Bake chicken in the preheated oven until no longer pink at the bone and the juices run clear, about 90 minutes. An instant-read thermometer inserted into the thickest part of the thigh should read 180 degrees F (82 degrees C).

Remove chicken from the oven, cover with a doubled sheet of aluminum foil, and allow to rest in a warm area for 10 minutes before slicing.