The leaves and grass clippings might work, just keep an eye out incase they breakdown too quickly and you need to top ofg. I've always used hay / garden straw for my garlic mulch. It lasts the winter and when I harvest the garlic I just mix it into the soil to continue to compost in place.
The one problem I keep running into with the hay is seeds, even though they are not supposed to have any, causing new hay to start growing. So there's some extra wedding that I need to do. It can be hard to distinguish from the garlic at first, but as they mature it becomes more obvious and I've learned how to more easily tell them apart.