I was watching this series of lectures on universal algebra on YouTube and the instructor, Charlotte Aten, mentioned that Øystein Ore studied lattices with the goal of using lattices as a unifying abstraction for mathematical structures. I don't remember which exact lecture she said this in, but she compares the goals of the lattice-based approach with category theory, which has been successful as a unifying abstraction.
I'm curious what the "lattice program" (so to speak) achieved, how it was perceived at the time, where it got stuck, and how it ended.