Season chicken: Preheat oven to 400°F. Sprinkle chicken evenly with salt and pepper.
Cook chicken: Heat oil in a large ovenproof skillet over medium-high. Place chicken, skin side down, in hot oil. Cook, undisturbed, until skin is deep golden-brown and crisp, 8 to 10 minutes. Transfer browned chicken, skin side up, to a large plate. Reduce heat to medium. Do not wipe skillet clean.
Cook lemons: Add lemon slices to drippings in skillet; cook over medium, until lightly browned, about 2 minutes, flipping halfway through cook time. Transfer lemons to a small plate. Do not wipe skillet clean.
Make sauce: Add garlic to skillet; cook over medium, stirring constantly, until fragrant, about 30 seconds. Add chicken stock and lemon juice to skillet; stir bottom of skillet to scrape up and loosen any browned bits. Add thyme sprigs and browned chicken, skin side up, to skillet.
Finish cooking chicken: Transfer skillet to preheated oven. Cook until thermometer inserted into thickest portion of chicken thigh registers 165°F, 18 to 20 minutes. Remove from oven, and immediately add butter to skillet. Stir with a wooden spoon or swirl the skillet until butter is fully melted and emulsified, 1 to 2 minutes. Return lemon slices to skillet. Garnish with thyme leaves, and serve.
