Set a barbecue to a medium heat. In a bowl, whisk together the yogurt and lemon juice, then stir in the dill. Season with salt and set aside.
Brush both sides of the courgette slices with olive oil, then carefully place on the hot grill. Cook on each side for 5–6 minutes until char lines appear and the slices have softened.
Use tongs to remove the courgette from the grill and place onto a serving plate. Season with black pepper and spoon over the lemon and dill yogurt.