Accurately predicting frictional performance of lubrication systems requires mathematical predictive tools with reliable lubricant shear-related input parameters, which might not be easily accessible. Therefore, the study proposes a semi-empirical framework to predict accurately the friction performance of lubricant systems operating across a wide range of lubricant regimes. The semi-analytical framework integrates laboratory-scale experimental measurements from a pin-on-disk tribometer with a unified numerical iterative scheme. The numerical scheme couples the effect of hydrodynamic pressure generated from the lubricant and interacting asperity pressure, essential along the mixed lubrication regime. The lubricant viscosity-pressure coefficient is determined using a free-volume approach, requiring only the lubricant viscosity-temperature relation as the input. The simulated rough surface contact shows transition in lubricant regimes, from the boundary to the elastohydrodynamic lubrication regime with increasing sliding velocity. Through correlation with pin-on-disk frictional measurements, the slope of the limiting shear stress-pressure relation $\gamma$ and the pressure coefficient of boundary shear strength m for the studied engine lubricants are determined. Thus, the proposed approach presents an effective and robust semi-empirical framework to determine shear properties of fully-formulated engine lubricants. These parameters are essential for application in mathematical tools to predict more accurately the frictional performance of lubrication systems operating across a wide range of lubrication regimes.