Four years ago, I read a book on the history of mathematics up to 1970 or so. It was very interesting up until the end. The last few chapters, though, were on lattices. The author claimed that lattices were taking math by storm, and that soon lattices would be one of the central objects in mathematics, and many other such claims similar to those now made in reference to category theory.

I couldn't find the book online, but I found references to similar ideas in this post:Good lattice theory books?

Question 1: Was lattice theory central to mid-twentieth century mathematics? Question 2: Is it central now?

Edit: A simpler question with more definite answers: did any mathematicians in the mid-1900s claim that lattice theory was vital or central to mathematics, and what arguments did they give?