  We analytically describe the properties of the s-wave holographic
superconductor with the Exponential nonlinear electrodynamics in the Lifshitz
black hole background in four-dimensions. Employing an assumption the scalar
and gauge fields backreact on the background geometry, we calculate the
critical temperature as well as the condensation operator. Based on
Sturm-Liouville method, we show that the critical temperature decreases with
increasing exponential nonlinear electrodynamics and Lifshitz dynamical
exponent, z, indicating that condensation becomes difficult. Also we find that
the effects of backreaction has a more important role on the critical
temperature and condensation operator in small values of Lifshitz dynamical
exponent, while z is around one. In addition, the properties of the upper
critical magnetic field in Lifshitz black hole background using Sturm-Liouville
approach is investigated to describe the phase diagram of the corresponding
holographic superconductor in the prob limit. We observe that the critical
magnetic field decreases with increasing Lifshitz dynamical exponent, z, and it
goes to zero at critical temperature, independent of the Lifshitz dynamical
exponent, z.
