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In the literature, people seem to predominantly look at lattices in nilpotent or reductive groups. Is there a result that gives a general description of a lattice in an arbitrary Lie group? Something ...

Edit: Thoughts updated (22/3/2021). I've come across with the following problem. Let $G=\mathbb{R}^s \ltimes_\varphi \mathbb{R}^k$ where $\varphi:\mathbb{R}^s\to \mathrm{Aut}(\mathbb{R}^k)=\mathsf{GL}(...

Let $V$ denote $\mathbb{Z}^{2g}$ with its standard integral symplectic form $\omega = \sum_{i=0}^{g-1}dx_{2i} \wedge dx_{2i+1}$ (or, the homology lattice of a genus $g$ surface with its intersection ...