In fusion devices, liquid lithium is increasingly employed as a plasma-facing material owing to high heat loads and neutron irradiation, as well as the necessity for impurity control in the plasma. Notably, addressing the retention of hydrogen and its isotopes deuterium and tritium is crucial for effective utilization of liquid lithium. To measure and control the hydrogen and deuterium content in liquid lithium, specialized permeation sensors and permeation extraction devices are essential. Consequently, there is a need for research on the permeation and diffusion of hydrogen in liquid lithium and permeable membranes. This paper introduces a model encompassing hydrogen adsorption, diffusion, and permeation in niobium membranes and liquid lithium. Experimental measurements of hydrogen adsorption in liquid lithium and hydrogen permeation in niobium membranes are presented. The scenarios are simulated using hydrogen transport module developed on COMSOL platform, resulting in a relatively good agreement with the experimental data.