Lattice VOA strong locality and net-identification conjecture

Let $L$ be an even positive definite lattice. The corresponding simple unitary lattice vertex operator algebra $V_L$ is strongly local, and the corresponding conformal net ${\mathcal A}_{V_L}$ coincides with the lattice conformal net ${\mathcal A}_L$ constructed in the cited work.

Lattice VOA conjecture.

$$V_L\text{ is strongly local},\qquad {\mathcal A}_{V_L}={\mathcal A}_L.$$

This conjecture would identify the conformal net obtained from a lattice vertex operator algebra with the independently constructed lattice conformal net. The source provides no resolution status.