Our collaborative work with the Hsieh group at CalTech was published. In this paper, a charge density wave instability is discovered as the spin-orbit Mott state of Sr3Ir2O7 is suppressed via La-substitution. As electrons are added to the material, a competing order parameter coupled to the lattice drives an electronic instability strongly coupled to the lattice. Some of our previous work discovered a lattice distortion that emerged as the Mott state collapsed, and this current paper proves that this lattice response is a secondary consequence of a competing charge density wave-like order that sets in. This demonstrates the correlated nature of the metallic state realized beyond the collapse of this weak spin-orbit Mott state.