Separate each chicken leg into the thigh and lower leg at the joint. Peel the skin from the thighs only and cut the skin into small pieces. Heat a frying pan over medium-high heat and cook the skin pieces, stirring occasionally, for 8-10 minutes until all the fat has rendered and the skin is golden and crispy. Season with salt and pepper. Transfer the crispy skin to a sieve set over a bowl to collect the rendered fat.
Pour 2 to 3 tablespoons of the rendered fat onto a large roasting dish. Arrange the chicken pieces (thighs and lower legs) on top of the fat. Distribute the potato wedges around the chicken. Scatter the capers, olives, several garlic cloves, and thyme sprigs over everything. Drizzle with olive oil and any remaining rendered chicken fat. Season with salt and pepper. Arrange the lemon slices on top of the chicken pieces.
Roast in a preheated oven at 200°C (392°F) on the middle rack for 30-45 minutes. Then reduce the oven temperature to 150°C (302°F) and continue roasting for another 30 minutes, until the chicken reaches an internal temperature of 74°C (165°F) when measured in the thickest part of the thigh.
Remove from the oven. Discard the lemon slices. Sprinkle the crispy skin pieces over the chicken and potatoes. Serve immediately.
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