Preheat a barbecue to medium-high heat. Drizzle the lamb with oil and sprinkle with salt and pepper. Cook on the barbecue for 30 minutes, turning every 10 minutes, until medium or cooked to your liking. Add the corn to the barbecue in the last 15 minutes of cooking and turn occasionally until charred.
Remove the lamb, cover with foil and rest for 10 minutes. Slice the corn from the cob.
Meanwhile, to make the avocado chimichurri, place quarter of an avocado, coriander, parsley, chilli, 1⁄4 cup olive oil and water in a small food processor and blend until finely chopped and well combined.
Cut the remaining avocado into large wedges and place in a serving bowl with the corn and radishes. Drizzle with olive oil and season with salt and pepper. Toss to combine.
To serve, slice the lamb, drizzle with the avocado chimichurri and serve with the avocado and charred corn salad.