Given a classic (not Residuated) lattice, with standard definition of partial order via lattice join and meet operations, is it possible to satisfy Galois equivalence
(x v y) < z <-> x < (y / z).
for some binary operation /?
Edit: One way to answer this is putting lattice axioms together with Galois condition into something like Mace4. Then finite model search reveals that lattice join v appears to have no adjoints, while meet ^ has. The question is more subtle, however: is there adjoint for lattice meet operation in any lattice model?