We report the results of a neutron powder diffraction study of the La0.62Li0.16TiO3 perovskite that determined the diffusion path of lithium cations at room temperature. At 77 K, the Li cations are located at the 2c site (Wycoff notation of the Cmmm space group) on the (002) La deficient layer, while, at room temperature, they are spread over a wide area and migrate following the 2c-4f-2c or 2c-2d-2c tie line on the (002) layer. The probability density of Li cations has a minimum between the 2c and 4f or between the 2c and 2d positions on the diffusion path in contrast to the previous reports where the bottleneck has been thought to be located at the 2c, 2d, and 4f positions. On the basis of the present structural model, the Li-cation conductivity is discussed in terms of a two-dimensional bond-percolation model for Li-cation diffusion. It was found that the vacancy at the La site is essential for the Li-cation conduction.