This paper is concerned with the existence results for generalized transition waves of space periodic and time heterogeneous lattice Fisher-KPP equations. By constructing appropriate subsolutions and supersolutions, we show that there is a critical wave speed such that a transition wave solution exists as soon as the least mean of wave speed is above this critical speed. Moreover, the critical speed we construct is proved to be minimal in some particular cases, such as space-time periodic or space independent.
