There's one I originally learned about in this excellent answer here at Math Overflow.

Complemented modular lattices satisfying a finiteness condition are exactly the lattice of subspaces of projective spaces. This raises the question of whether we can reverse the process, and associate a geometry with every modular lattice satisfying the same finiteness condition. There are several versions of this idea, but one particularly simple one is found in Benson and Conway, Diagrams for Modular Lattices.

All of the versions share two basic ideas. We already have one clue for what a geometry should look like for a distributive lattice by considering Birkhoff's representation theorem -- join-irreducible elements are points, and these points have a natural partial order on them. What's new in the modular case is that we also have lines, which are when you have three or more join-irreducible elements such that any two of them have the same join. A complete version of this idea was already found in Faigle and Hermann, but Benson and Conway is essentially a rediscovery, but the paper itself explains the idea very clearly.

Since Conway was more famous for his work on the other kind of lattice, I was curious how many of them were about this kind of lattice. Based on a quick search of paper titles it looks like the answer is: one.