Lubrication flows between two solid surfaces can be found in a variety of biological and engineering settings. In many of these systems, the lubricant exhibits viscoelastic properties, which modify the associated lubrication forces. Here, we experimentally study viscoelastic lubrication by considering the motion of a submerged cylinder sliding down an incline. We demonstrate that cylinders move faster when released in a viscoelastic Boger liquid compared to a Newtonian liquid with similar viscosity. Cylinders exhibit pure sliding motion in viscoelastic liquids, in contrast to the stick-slip motion observed in Newtonian liquids. We rationalize our results by using the second-order fluid model, which predicts a lift force on the cylinder arising from the normal-stress differences. The interplay between viscoelastic lift, viscous friction, and gravity leads to a prediction for the sliding speed, which is consistent with our experimental results for weakly viscoelastic flows. Finally, we identify a remarkable difference between the lubrication of cylindrical and spherical contacts, as the latter do not exhibit any lift for weak viscoelasticity.