Haar measure conjecture for symplectically integral lattices of fixed type

Let $D=\operatorname{diag}(d_1,\ldots,d_n)$ be a type, and let $\mathcal{L}\subseteq\mathcal{L}^{\perp}\subseteq\mathbb{R}^{2n}$ be a symplectically integral lattice of type $D$. Haar measure conjecture. There exists a Haar measure over all symplectically integral lattices $\mathcal{L}\subseteq\mathcal{L}^{\perp}\subseteq\mathbb{R}^{2n}$ with type $D$. The conjecture would provide a natural measure on the space of such GKP-code lattices, supporting the existence and study of typical codes. The surrounding discussion establishes existence results for good families and fixed type, but does not establish this measure-theoretic statement.