Chudnovsky–Edwards–Kim–Scott–Seymour orientation conjecture for lattice families

Let $G=(V,E)$ be a tree, and let $\mathcal{L}$ be a lattice family over ground set $V$ such that $|\delta(U)|\geq 2$ for every $Uin \mathcal{L}\setminus {\emptyset,V}$. An orientation $D$ of $G$ has outgoing and incoming arc sets $\delta_D^+(U)$ and $\delta_D^-(U)$ across each such set.

Chudnovsky–Edwards–Kim–Scott–Seymour conjecture. There exists an orientation $D$ of $G$ such that $\delta_D^+(U)$ and $\delta_D^-(U)$ are both nonempty for every $Uin \mathcal{L}\setminus {\emptyset,V}$.

The source attributes this conjecture to Chudnovsky, Edwards, Kim, Scott, and Seymour. Its status is not resolved in the supplied text.