  Strongly correlated insulators are broadly divided into two classes:
Mott-Hubbard insulators, where the insulating gap is driven by the Coulomb
repulsion $U$ on the transition-metal cation, and charge-transfer insulators,
where the gap is driven by the charge transfer energy $\Delta$ between the
cation and the ligand anions. The relative magnitudes of $U$ and $\Delta$
determine which class a material belongs to, and subsequently the nature of its
low-energy excitations. These energy scales are typically understood through
the local chemistry of the active ions. Here we show that the situation is more
complex in the low-dimensional charge transfer insulator
Li$_\mathrm{2}$CuO$_\mathrm{2}$, where $\Delta$ has a large non-electronic
component. Combining resonant inelastic x-ray scattering with detailed
modeling, we determine how the elementary lattice, charge, spin, and orbital
excitations are entangled in this material. This results in a large
lattice-driven renormalization of $\Delta$, which significantly reshapes the
fundamental electronic properties of Li$_\mathrm{2}$CuO$_\mathrm{2}$.
