  Lubrication flows appear in many applications in engineering, biophysics, and
in nature. Separation of surfaces and minimisation of friction and wear is
achieved when the lubrication 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 timescale of loading becomes comparable to the
rheological timescale. We derive asymptotic relations between lift force and
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.
