Large modulus gear-rack mechanism has strong bearing capacity. They are often used in heavy-duty equipment, i.e. for heavy load lifting. This study is focused on the ultra large modulus heavy duty open gear-rack drive mechanism of the Chinese "Three Gorge Dam" ship lift, of which lubrication design and management plays a critical role in safe operation and service life extension of the mechanism. Against the currently adopted manual oiling which raises concerns from ineffective lubrication, high lubricate wastes as well as risks of maintainers, this study aims to propose lean lubrication design method based on parametric modeling and numerical analysis. A three-dimensional linear contact hybrid elastohydrodynamic lubrication model was established to characterize lubrication behavior under effects of contact area size and morphology. With the EHL model, lean oil supply conditions were exploited based on effective lubricating oil thickness. Given the uncertainty and complexity of lubrication state in actual working conditions, texture design was then proposed for better tribological performance under starved lubrication conditions. The proposed models and methods were applied to the gear-rack drive of the Chinese “Three Gorge Dam” ship lift. The numerical results suggested the proposed lean lubrication plan may consume 4.13% less lubricating oil in one mesh cycle than that calculated by conventional methods. The reduction of lubricating oil consumption can be larger if the high waste from oil oversupply by manual oiling is considered. The output of case study may serve as the basis of further development of lean lubrication system for the gear-rack drive mechanism.