Let chicken and 1 tablespoon butter stand at room temperature for 30 minutes. Preheat oven to 425 degrees. Remove and discard the plastic pop-up timer from chicken if there is one. Remove the giblets and excess fat from the chicken cavity. Rinse chicken inside and out under cold running water. Dry chicken thoroughly with paper towels. Tuck the wing tips under the body. Sprinkle the cavity of the chicken liberally with salt and pepper, and set aside.
In the center of a heavy-duty roasting pan, place onion slices in two rows, touching. Place the palm of your hand on top of lemon and, pressing down, roll lemon back and forth several times. This softens the lemon and allows the juice to flow more freely. Pierce entire surface of lemon with a fork. Using the side of a large knife, gently press on garlic cloves to open slightly. Insert garlic cloves, thyme sprigs, and lemon into cavity. Place chicken in pan, on onion slices. Cut about 18 inches of kitchen twine, bring chicken legs forward, cross them, and tie together.
Spread the softened butter over entire surface of chicken, and sprinkle liberally with salt and pepper. Place in the oven, and roast until skin is deep golden brown and crisp and the juices run clear when pierced, about 1 1/2 hours. When chicken seems done, insert an instant-read thermometer into the breast, then the thigh. The breast temperature should read 180 degrees and the thigh 190 degrees.
Remove chicken from oven, and transfer to a cutting board with a well. Let chicken stand 10 to 15 minutes so the juices settle. Meanwhile, pour the pan drippings into a shallow bowl or fat separator, and leave onions in the pan. Leave any brown baked-on bits in the bottom of the roasting pan, and remove and discard any blackened bits. Using a large spoon or fat separator, skim off and discard as much fat as possible. Pour the remaining drippings and the juices that have collected under the resting chicken back into the roasting pan. Place on the stove over medium-high heat to cook, about 1 minute. Add chicken stock, raise heat to high, and, using a wooden spoon, stir up and combine the brown bits with the stock until the liquid is reduced by half, about 4 minutes. Strain the gravy into a small bowl, pressing on onions to extract any liquid. Discard onions, and stir in the remaining tablespoon of cold butter until melted and incorporated. Untie the legs, and remove and discard garlic, thyme, and lemon. Carve, and serve gravy on the side.