On a side burner or stove top, bring the potatoes to the boil in hot water. Boil for 20 minutes, or until softened enough to pierce with a knife. Drain all the liquid from the potatoes.
Prepare the barbecue for indirect cooking over medium heat (190°C to 230°C). If using a Weber Q barbecue, set up your barbecue with a convection tray and a trivet.
Add the olive oil, salt, pepper, rosemary and lemon cubes to the pot with the potatoes. Vigorously shake the pot to roughen the potatoes and evenly coat with the olive oil and seasonings.
Roast the potatoes over indirect medium heat for 40 to 50 minutes, with the lid closed, or until golden.
If desired, finish with an extra season of salt and pepper.