Season the lamb on both sides, drizzle with olive oil.
Heat a griddle pan on high heat and add the lamb and lemon, halved side down. Cook the lamb for 4-5 minutes on each side or until cooked to your liking. Cook the lemon until charred.
Remove lamb and rest for 10 minutes.
To cook the potatoes, par boil in salted water for 10 minutes. Remove from the water and cut in half.
Add a tablespoon of olive oil to a pan on medium heat. Fry the potatoes with the butter, thyme and garlic until golden.
Serve the lamb and potatoes on a plate with the charred lemon.