I was thinking the same as Celia and Silversurfer, maybe an Allium. I'm not sure which of the larger ones have offsets but some Alliums do. Lawn bowling balls are apparently 4-5" in diameter. RMAdamson, if you could post a picture it would help. Also what country you are in (presumably not USA because measurement given in metric) and whether this plant is growing in the wild or a garden.
Here are pictures of some alliums in tne NGA database, does it look like any of these?
http://garden.org/plants/brows...