In this paper, we derive a lattice model for a single species in a two dimensional patchy environment with infinite number of patches connected locally by diffusion. Under the assumption that the death and diffusion rates of the mature population are age independent, we show that the dynamics of the mature population is governed by a lattice delay differential equation with global interactions. We obtain the existence of monotone travelling waves for wave speeds c > c* by the standard monotone iteration method and the construction of upper-lower solutions. We show that the minimal wave speed c* is also the asymptotic speed of propagation.