The lubrication regimes of a contact pair escapement-ruby pallet of a Swiss lever escapement have been investigated combining the theory of fluid lubrication with a well-established kinematic and inverse dynamic multibody model. The kinematic analytical results have been confronted with experimental measurements. The developed model allows to easily obtain, for the three operating phases of the Swiss lever escapement, the relative speed and the contact forces and, by considering a hydrodynamic lubrication regime, the lubricant minimum film thickness and the coefficient of friction. The presented formulation allows to study the influence of crucial technical parameters in the Swiss lever escapement lubrication. The spout radii of curvature have been identified as the optimal parameters to control the lubrication regimes in the pallet/escapement contacts. In that sense, an interesting result is that the lubrication regime moves away from the boundary lubrication by increasing these radii.