Nuclear Pressurised Water Reactors (PWRs) use zirconium alloys as a fuel cladding, preventing the cooling water, at elevated pH using lithium hydroxide, from interacting with the fuel. Boron, as boric acid, is added to the coolant as a reactivity shim. Future reactor designs are considering removing soluble boron reactivity control to aid plant simplification. The presence of lithium in the absence of boron in the coolant has, however, been found to accelerate the corrosion of zirconium-based alloys under certain conditions and the mechanisms by which this occurs is under investigation. The ingress of lithium into the bulk oxide layer of zirconium alloy has been addressed in a previous study and was found to be unlikely. Here, atomistic simulations were used to produce Brouwer diagrams from which the solubility of lithium in amorphous structures representing complex grain boundaries have been predicted. The solubility of lithium in these amorphous structures is predicted to be high and will produce an elevated concentration of oxygen defects within the amorphous structure. This could offer a mode for transport of oxygen to the metal oxide interface and, potentially, offer a mechanism or part of a mechanism for observed lithium-accelerated corrosion of Zr-based alloys.