If I recall correctly, it's targeting the larval stages that live in the sediments. So there's an example where the lampricide is applied with that specific life stage in mind.
Normally, we don't look at it that way. Where eradication has been applied in other parts of the world, there's been an attempt to do it before the species has time to disperse rapidly. If it does disperse rapidly, then you're always going to be putting out fires. Also, you have to consider prioritization of species for eradication—in other words, those species most likely to be eradicated—rather than wasting your effort. Species have been identified as priorities for eradication when it's been understood that they can't disperse very quickly, such as certain snails or parasites of these snails. There have been examples on abalone farms of successful eradication of a parasite because it was understood that this thing was a crawling invertebrate, and that therefore it couldn't get very far. So they had time and were likely to be successful if they invested the effort in doing it.
So in that sense, once the invasion has proceeded, once you have a population there, you can make decisions based on its life history, perhaps even specific to certain life stages. You can decide whether it is worth the effort to attempt an eradication, with some potential collateral damage to the rest of the community, or whether it is just going to be a completely controlled operation from now on. These stages where you make the judgments as to prevention, eradication, or chronic control usually depend on how far the species has progressed in its population buildup, which is a function of time.