Why not just use the engines that come with the starship? In any case, both shipping the asteroid bit by bit inside a rocket or converting the entire asteroid i

Why not just use the engines that come with the starship? In any case, both shipping the asteroid bit by bit inside a rocket or converting the entire asteroid into a rocket will need basically the same amount of fuel. You would need to bring over the lithium ore processing equipment as well, so you only need to transport refined lithium metal back to earth. You might even be able to use the non-lithium parts of the asteroid as reaction mass in that case.