Preheat the oven to 425° F and line a rimmed baking sheet with parchment paper. Next, grab a big bowl and cutting board. Chop all the vegetables (onion, butternut squash, potatoes, beets) into 2-inch pieces. Toss the vegetables with the olive oil and salt then evenly layer the mixture across the sheet pan. Top with lemon rounds and thyme sprigs. Place the chicken drumsticks on top of the vegetable mix. Sprinkle chicken with salt and pepper.
Roast the sheet pan dinner for 45 minutes. If you’d like, turn the broiler on for the last few minutes to brown the chicken skin. While the chicken cooks, mix all the yogurt sauce ingredients together. Serve the drumsticks with a bowl of yogurt sauce for dipping.