If using wooden skewers, soak them in water for 30 minutes so they do not burn.
Cut the chicken into 3 cm (1 1/4 inch) cubes and toss with half the lemon juice, half the garlic-infused oil, the oregano, salt and pepper. Marinate for at least 15 minutes or up to 24 hours in the fridge.
Preheat the oven to 220°C (425°F). Toss the potato wedges with the rest of the oil and lemon juice and a pinch of salt and spread on a lined tray.
Roast the potatoes for 25 minutes, turning once, until crisp and golden.
Thread the chicken and pepper chunks onto the skewers. Preheat the grill or a grill pan over medium-high heat, about 200 to 230°C (400 to 450°F), and oil the grates.
Grill the skewers for 10 to 12 minutes, turning every 3 minutes, until charred in spots and the chicken reaches 74°C (165°F) inside.
Squeeze the grated cucumber dry and mix it with the lactose-free yogurt and chopped dill.
Serve the skewers with the lemon potatoes and the cucumber yogurt.
Tips
Soak wooden skewers in water for 20 minutes so they do not burn.