Heat your oven to 450 degrees F. Spray a large dark roasting pan (ideally) or rimmed sheet pan with oil.
Leave the skin on the chicken and pat it dry with a paper towel (no need to rinse it first, but you want to make sure you get rid of excess moisture so it doesn't steam in the oven instead of getting crisp). Arrange the chicken pieces in the pan in a single layer. Wash your hands well.
Rinse your sweet potatoes and peel off the skin with a vegetable peeler. Cut off the ends and discard them. Slice your potatoes into rounds about 1 ½ inches thick. Add your sweet potatoes around the chicken in your pan.
If using broccoli, rinse it and pat it dry. Cut off most of the thick stems, leaving the florets and about three inches of the stems in place. Separate the florets, leaving the broccoli in clusters. (If they're too thin, they'll burn.) Add them to your pan, on top of your sweet potatoes.
If using zucchini, rinse and pat them dry. Slice off the ends and discard them. Slice the zucchini into rounds at least two inches thick and add them to your pan, on top of the sweet potatoes. It's best not to let them touch the bottom of the pan, or they can turn out soggy.
Peel your red onion and cut off the ends. Cut the onion into quarters, and if desired, cut those quarters in half. You should have thick sections of onion to add on top of your chicken and vegetables.
Evenly drizzle your olive oil over the chicken and vegetables. Add your seasoning to your taste.
Bake, uncovered for 40-45 minutes. After the first 20 minutes, flip over your sweet potatoes and stir around your veggies.
After 40 minutes of baking (or a little sooner if your oven runs hot), you will need to remove the broccoli and place it a dish, covered with foil, so it doesn't burn. The zucchini should be able to hold up to a little more baking. Check to see if your chicken is cooked through. It should not have any pink inside.
If needed, and to help crisp the skin, bake for five minutes more. At this point, you can let the chicken and vegetables rest on your stovetop, or, if you want the skin to get crispier, you can place the pan under the broiler for 1-2 minutes, watching it constantly so it doesn't burn.
When your pan is out of the oven, squeeze on the juice of half a lemon that hasn't been roasted. (It will have better flavor.) Loosely cover the pan with foil and let the chicken rest for a few minutes before serving. Stir the potatoes and vegetables to coat them with the pan juices before serving with the chicken.
Store leftovers in the refrigerator for up to four days.
A dark roasting pan will help the vegetables and sweet potatoes to brown better than a sheet pan will. If you only have a sheet pan, I recommend making this with broccoli instead of zucchini.
If using fewer chicken thighs, use less oil. Try 2 tablespoons.
If you want to use bone-in chicken breasts, check to see if they are done after 35-40 minutes. Remove them from the oven as soon as they are cooked through, so they don't get dry. If you also have some dark meat in the pan, you may want to cook those pieces longer; if not, your dinner will be done as soon as the chicken is cooked.
If you want to add half a lemon to roast in the pan, go ahead. It looks nice. But I find that squeezing on the juice of half a raw lemon provides better flavor.