The plague threatened pasture for livestock and rice crops - the main staple in Madagascar, the FAO said.
The disappearance of the lake is being caused by climate change, population pressure and natural variations in climate, the FAO said.
The FAO said earlier that the "true enormity of this human tragedy" had emerged for the first time from the study, done jointly with Fews Net.
The Locust Control Centre in Madagascar had treated 30, 000 hectares of farmland since last October, but a cyclone in February made the situation worse, the FAO said.
"Currently, about half the country is infested by hoppers and flying swarms - each swarm made up of billions of plant-devouring insects, " the FAO said in a statement.
Once one of the biggest bodies of water in the world, it could disappear entirely in about 20 years, the FAO said, citing forecasts from the U.S. National Aeronautics and Space Administration.
Even more help is urgently needed, FAO officials said, in order to prevent an even worse humanitarian crisis tied to the locust plague.
"There is a potential for a situation to develop like we have back in 2007-2008, " said FAO senior economist and grain analyst Abdolreza Abbassian.
"The severe deterioration of maize crop prospects in the US following extensive drought damage pushed up maize prices by almost 33% in July, " said the FAO.
The solution, FAO Director-General Jacques Diouf said, is increasing production and productivity in the low-income, food-deficit countries.
Older farmers who remember that crisis and see the big swarms nowadays "stop farming, because they know that it's useless, " said Huynh, the FAO's emergency and rehabilitation coordinator in Madagascar.
"This is not some gentle wake-up call - it's the same global alarm that's been screaming at us since 2008, " said Hannah Stoddart, Oxfam's head of economic justice policy, regarding the FAO data.
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