  We present Density Matrix Renormalization Group calculations of the
ground-state properties of quarter-filled ladders including static
electron-lattice coupling. Isolated ladders and two coupled ladders are
considered, with model parameters obtained from band-structure calculations for
$\alpha^\prime$-NaV$_2$O$_5$. The relevant Holstein coupling to the lattice
causes static out-of-plane lattice distortions, which appear concurrently with
a charge-ordered state and which exhibit the same zigzag pattern observed in
experiments. The inclusion of electron-lattice coupling drastically reduces the
critical nearest-neighbor Coulomb repulsion $V_c$ needed to obtain the
charge-ordered state. No spin gap is present in the ordered phase. The charge
ordering is driven by the Coulomb repulsion and the electron-lattice
interaction. With electron-lattice interaction, coupling two ladders has
virtually no effect on $V_c$ or on the characteristics of the charge-ordered
phase. At $V=0.46\eV$, a value consistent with previous estimates, the lattice
distortion, charge gap, charge order parameter, and the effective spin coupling
are in good agreement with experimental data for NaV$_2$O_5$.
