We continue our study of holographic transport in the presence of a background lattice. We recently found evidence that the presence of a lattice induces a new intermediate scaling regime in asymptotically $AdS4$ spacetimes. This manifests itself in the optical conductivity which exhibits a robust power-law dependence on frequency, $\sigma \sim \omega -2/3$, in a "mid-infrared" regime, a result which is in striking agreement with experiments on the cuprates. Here we provide further evidence for the existence of this intermediate scaling regime. We demonstrate similar scaling in the thermoelectric conductivity, find analogous scalings in asymptotically $AdS5$ spacetimes, and show that we get the same results with an ionic lattice.