Lubrication flows appear in many applications in engineering, biophysics and nature. Separation of surfaces and minimisation of friction and wear is achieved when the lubricating fluid builds up a lift force. In this paper we analyse soft lubricated contacts by treating the solid walls as viscoelastic: soft materials are typically not purely elastic, but dissipate energy under dynamical loading conditions. We present a method for viscoelastic lubrication and focus on three canonical examples, namely Kelvin-Voigt, standard linear and power law rheology. It is shown how the solid viscoelasticity affects the lubrication process when the time scale of loading becomes comparable to the rheological time scale. We derive asymptotic relations between the lift force and the sliding velocity, which give scaling laws that inherit a signature of the rheology. In all cases the lift is found to decrease with respect to purely elastic systems.