The diffusion of He through both H2O and D2O amorphous solid water (ASW) has been measured between 55 and 110 K. We find the diffusion rate is dependent on the isotopic composition of the ASW lattice. This lattice isotope effect is the "inverse" of a normal isotope effect in that diffusion is faster in the heavier (D2O) isotope. Transition state theory calculations show that the inverse isotope effect is due to a tight transition state and predominantly arises from the zero-point vibrational energy associated with the frustrated rotational modes of water in the lattice.