In a small bowl, combine lemon juice, sugar, vinegar and water; set aside.
Place figs and lemon slices in the bottom of a large baking tray. Arrange chicken thighs on top, then pour vinegar mixture over chicken. Finally, sprinkle with salt and dried parsley to taste.
Bake in preheated oven for 50 minutes, basting frequently (turn figs if they begin to brown).
With a slotted spoon, remove chicken, figs and lemon slices from baking dish and place on a warm platter. Skim fat from cooking juices, then pour over chicken as sauce. Garnish with fresh parsley and serve.