In a bowl, whisk together 1/3 cup olive oil, 1/3 cup lemon juice, 1 T Greek seasoning, 1 tsp Spike or other all-purpose seasoning, and 1/2 tsp dried thyme to make the marinade.
Reserve 1/4 cup of the marinade in a small container and set aside for brushing later.
Trim excess skin and fat from the chicken thighs and make a few small slits in the skin of each thigh.
Place the chicken thighs in a zip-top bag or shallow dish with the remaining marinade, seal, and marinate in the refrigerator for 4–8 hours or up to all day.
About 30 minutes before cooking, remove the chicken from the fridge, drain in a colander, and let it come to room temperature while you preheat the oven to 425°F (220°C).
Arrange the chicken thighs in a single layer on a large sheet pan and roast for 8 minutes.
While the chicken starts roasting, trim the ends off the green beans and cut them in half. Halve the cherry tomatoes.
Remove the sheet pan and blot any released liquid from the chicken with paper towels. Add the prepared green beans to the pan and brush the chicken and beans with the reserved 1/4 cup marinade. Season with fresh-ground black pepper and a little salt if desired.
Return the pan to the oven and roast 14 minutes more.
After 14 minutes, when the chicken is beginning to brown, tuck the halved cherry tomatoes around the chicken and green beans, keeping items as much in a single layer as possible.
Roast about 6 minutes more, or until the chicken is cooked through and the green beans are tender.
Sprinkle the hot dish with crumbled feta cheese and serve immediately.