Via numerical and analytical methods, the effects of the Lifshitz dynamical exponent z on the holographic superconductor models are studied in some detail, including s-wave and p-wave models. Working in the probe limit, we calculate the condensation and conductivity in both Lifshitz black hole and soliton backgrounds with a general z. For both the s-wave and p-wave models in the black hole backgrounds, as z increases, the phase transition becomes difficult and the conductivity is suppressed. For the Lifshitz soliton background, when z increases, the critical chemical potential increases in both the s-wave model (with a fixed mass of the scalar field) and p-wave model. For the p-wave model in both the Lifshitz black hole and soliton backgrounds, the anisotropy between the AC conductivity in different spatial directions is suppressed when z increases. In all cases, we find that the critical exponent of the condensation is always 1/2, independent of z and spacetime dimension. The analytical results from the Sturm–Liouville variational method uphold the numerical calculations. The implications of these results are discussed.