What can be done when an invasive plant is taking over a lake? Removing it is often not an option; many aquatic invasives spread vegetatively, which means that if you break up stems you aren't killing the plant, you're just increasing the potential for the species to restablish in a new area or cling to a boat and find refuge in a nearby body of water. There are rarely any options for eradication that won't cause serious disturbance to the rest of the lake's flora and fauna. Often a decision is made to wipe out almost everything in the lake and "start from scratch".
South Australia is taking the herbicide route, using a combination of chlorine and copper sulfate to rid the West Lakes of Caulerpa taxifolia, according to this story from news.com.au. Some parties are concerned about the major impact this could have on all lake life, but after reading how aggressive Caulerpa can be, I don't blame them for making this decision. You can read more about aquatic plant management here.