Niobium tungsten oxides with crystallographic shear structures form a promising class of high-rate Li-ion anode materials. Lithium diffusion within these materials is studied in this work using density functional theory calculations, specifically nudged elastic band calculations and ab initio molecular dynamics simulations. Lithium diffusion is found to occur through jumps between 4-fold coordinated window sites with low activation barriers (80-300 meV) and is constrained to be effectively one-dimensional by the crystallographic shear planes of the structures. We identify a number of other processes, including rattling motions with barriers on the order of the thermal energy at room temperature, and intermediate barrier hops between 4-fold and 5-fold coordinated lithium sites. We demonstrate differences regarding diffusion pathways between different cavity types; within the ReO3-like block units of the structures, cavities at the corners and edges host more isolated diffusion tunnels than those in the interior. Diffusion coefficients are found to be in the range of 10-12 to 10-11 m2 s-1 for lithium concentrations of 0.5 Li/TM. Overall, the results provide a complete picture of the diffusion mechanism in niobium tungsten oxide shear structures, and the structure-property relationships identified in this work can be generalized to the entire family of crystallographic shear phases.