Hi,
Lily of the valley can become a very agressive ground cover and unfortunately about the only way that they can be prevented from moving into areas not wanted is the old fashioned way - digging ouot the offending plants as they appear. Using edgings or borders such as the plastic or metal types don't afford much control because they will simply grow underneath them. If continuous cutting back is not a good option then removing the entire planting from the bed is called for and then relocating to an area where an aggressive goundcover is not such a bad thing.
