Preheat the oven to 200 degrees C. In a small bowl whisk the garlic, lemon juice and olive oil to combine. Season with salt and pepper to taste.
Place the lamb racks on a large roasting tray and pour over the garlic mixture. Turn the racks to coat completely. Roast for 20 minutes for medium rare or until cooked to your liking. Remove from the oven, cover loosely with foil and allow to rest for 5-10 minutes.
Meanwhile, in a small saucepan combine the caster sugar, vinegar, water and half the mint. Bring to the boil and simmer for 5 minutes until it thickens slightly. Let it sit for 15 minutes to infuse the flavours. Strain the leaves from the sauce (they will have discoloured). Stir the remaining fresh mint leaves into the sauce and serve immediately with the lamb.