We present a one-dimensional model for diffusion in a fluctuating lattice; that is a lattice which can be in two or more states. Transitions between the lattice states are induced by a combination of two processes: one periodic deterministic and the other stochastic. We study the dynamics of a system of particles moving in that medium, and characterize the problem from different points of view: mean first passage time (MFPT), probability of return to a given site ($P_{s_0}$), and the total length displacement or number of visited lattice sites ($\Lambda$). We observe a double {\it resonant activation}- like phenomenon when we plot the MFPT and $P_{s_0}$ as functions of the intensity of the transition rate stochastic component.