Lattice theory was not central, and is not central now. 

I think that the problem with lattice theory is that, although lattices appear everywhere in mathematics, they usually appear as *objects* not as a *category*. In other words, the mapping that assignes lattices to objects of a category $\mathbf C$ is often not an object part of a functor $\mathbf{C}\to \mathbf{Lat}$, where by $\mathbf{Lat}$ I mean the category of lattices with $\vee,\wedge$-preserving maps as morphisms. Usually, we only have a functor $F:\mathbf{C}\to\mathbf{Pos}$, that has only lattices in its range. 

For example, it is well known that the matroids are "the same thing" as finite atomistic semimodular lattices. But this is not an equivalence of categories -- there is not enough arrows on the lattice side. Of course, we can add new arrows, but then we are outside of $\mathbf{Lat}$.