If finite lattices $L_1,L_2$ have Hasse diagrams that are isomorphic as undirected graphs, must $L_1$ and $L_2$ be isomorphic?

NOTE: Sam Hopkins points out that the answer is “no” because there are lattices that are not isomorphic to their duals. I would like to know if this “which way is up?” ambiguity is the only obstacle to reconstructing a lattice from its Hasse diagram (viewed as an undirected graph).

directedgraph, that is enough to recover the poset (and the lattice property is irrelevant). I suppose you could ask, how many of the edge directions do you need to know. $\endgroup$3more comments