For the chicken: Season the chicken cavity with salt and pepper, to taste. Stuff the chicken cavity with the shallot, half the thyme, and lemon zest. Set a v-rack or regular rack in a roasting pan, and brush chicken with a bit of the olive oil. Whisk the honey and remaining oil in a small bowl. Dip the remaining thyme in the mixture and use it to brush the chicken all over with the honey mixture. Season bird with salt and pepper, to taste.
Tuck the wings under the back, cross the legs, and tie them with kitchen string. Place the chicken breast side down on the rack and roast until the back is golden brown, about 35 to 40 minutes. Remove the pan from the oven and turn the chicken breast side up. Cut the string where it holds the legs together and open up the legs a bit. Baste the chicken with the pan drippings, using the thyme sprigs as a brush. Roast the chicken again until the breast is golden brown and a meat thermometer inserted in the thigh registers 170 degrees F., 20 to 25 minutes more. Transfer the chicken to a carving board, and let it rest 10 minutes before carving.
For the sauce: Remove the rack from the roasting pan. Put the pan over medium-high heat, add the water, and stir with a wooden spoon to release the brown bits that cling to the pan. Strain the pan drippings into a small bowl and spoon off the fat. Whisk in the lemon juice, olive oil, honey, shallot, thyme, salt, and pepper to taste. Carve the chicken and serve drizzled with the sauce.