Lobsters are genetically related to mosquitos not roaches. Based on the following study:
Pesticides
In 1999, West Nile virus arrived in the New York area, and two pesticides and one solid chemical were used to kill mosquitoes near Long Island Sound. Scientists do not know the concentration of those pesticides in the Sound just after they were applied. But they are beginning to know what two of those pesticides do to lobsters in a laboratory.
One of the many studies of pesticides and lobsters is headed by Sylvain De Guise, an assistant professor in the Department of Pathobiology and Veterinary Science at the University of Connecticut. He said that he and colleagues have found that malathion - the pesticide sprayed in New York - kills at least half of the lobsters in a test group at a concentration of 38 parts per billion.He did his study because he suspected a connection between mosquito spraying and lobster deaths.
If you put enough malathion in the water, it's going to kill lobsters, he said. The study suggests that because malathion breaks down within a few days, both in the water and in lobster tissue, only lobsters in the vicinity of the spraying would have been harmed.
https://www.nytimes.com/2004/03/28/nyregion/closing-in-on-the-killer-of-the-lobsters.html