Heat your oven to 425 F.
In a small roasting pan, toss sliced onions, 5/6 of the lemon slices, salt, pepper, and about 1 tbs olive oil to coat.
Disseminate coated onions and lemons evenly across the pan.
As carefully as possible, clean your chicken and pat it dry.
Stuff the chicken cavity with the reserved top and bottom of the lemon, the last 1/6 of the lemon, and the garlic halves.
Place your stuffed chicken on top of the onion and lemon mixture.
Wash your hands and your kitchen surfaces like crazy.
Pour a bit of olive oil over the top of the chicken and use a brush to coat the chicken with the oil.
Sprinkle pepper and a bit of salt over the top of the chicken.
Wash your hands and your surfaces like crazy, once again.
Roast the chicken for 45-75 minutes, depending upon the chicken's size.
The breast should read 155F and the leg and thigh should read 180F.
Remove the chicken from the pan of onions, lemons and drippings and let it rest on a cutting board.
Remove the 5/6 lemon segments from the pan and compost/discard them.
Add your broth [or water/bouillon] and [optional wine] to the pan of onions and drippings.
Set this pan over medium-high heat.
Using a wooden spoon or flat whisk, pick up the brown and burnt bits from the side of the pan.
Add a tablespoon of flour (shake or even sift it over the gravy to avoid lumps) to thicken the mixture.
Cook until the broth and onions begin to form a thick-ish gravy.
Pour the gravy and onions into a small bowl or gravy boat.
[Use a sieve to separate the gravy from the onions if you would like to serve them separately.]
Remove the garlic and lemon bits from the inside of the chicken and compost/discard them.
Slice the chicken and serve with the gravy.