Preheat the oven to 350 degrees F. Discard the giblets from the chicken's cavity and pat the chicken dry with paper towels.
Put the goat cheese, rosemary, lavender, lemon zest, and thyme in a food processor fitted with the steel blade attachment. Pulse until smooth.
Starting at the chicken's neck, carefully slide your fingers under the skin creating a pocket. Stretch your fingers down towards the thighs and extend the pocket as far as you can reach over the thigh meat. Spread the cheese mixture as evenly as you can over the breast and thigh meat.
Place the lemon halves inside the cavity of the chicken, truss the chicken and tuck the wings behind its back.
Rub a generous amount of salt and pepper over the skin and place in a shallow roasting pan just large enough for the chicken. Drizzle with olive oil. Roast, basting with pan juices several times, for about 1½ hours or until a thermometer inserted into the breast reads 165 degrees. Tent with foil and rest for 10 minutes before carving.