Preheat the oven to 450°F (232°C).
In a small bowl, whisk together 1/4 cup lemon juice, 1/3 cup olive oil, smashed garlic, 2 tsp salt, 1 tsp black pepper, chopped rosemary, chopped thyme, and snipped sage; set the lemon-garlic mixture aside.
Heat a large roasting pan or baking sheet over two stove-top burners on medium-high and add 2 tbsp olive oil.
Season the chicken drumsticks with a little additional salt and pepper, then add them to the hot pan and brown on all sides, turning often, about 7–10 minutes.
Add the potatoes to the pan, arrange lemon slices among the chicken and potatoes, and pour the reserved lemon-herb mixture evenly over everything.
Transfer the pan to the preheated oven and roast for 45–50 minutes, or until the chicken is cooked through and browned and the potatoes are tender.
Remove from the oven and let rest a few minutes before serving.