Supposedly, all he was responsible for was offering it. He sends letters to leaders of a few countries, and they, for the most part, reject him. So, then he says that the world is going to go through some terrible times that will force the people of the world to unite, that's the lesser peace.
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Lesser Peace will initially be a political unity arrived at by decision of the various governments of the world. The unity of nations can be taken as that unity which arises from a recognition among the peoples of the various nations, that they are members of one common human family.
I don't think the world is ready to try and unite on a world scale. People are way too divided over lots of stuff. And some of those things are so important to people that they will fight over them. In fact, in a lot of ways, I think some of the Baha'is are adding to the divisions between people. I agree with you way more than I agree with some of them. But should we at least listen to the Baha'i plan or keep ignoring it? One problem I see is that the Baha'i plan expects the nations to disarm. As the world is today, that ain't gonna happen.