Parsec-scale VLBA images of BL Lac at 15 GHz show that the jet contains a permanent quasi-stationary emission feature 0.26 mas (0.34 pc projected) from the core, along with numerous moving features. In projection, the tracks of the moving features cluster around an axis at a position angle of -166.6{deg} that connects the core with the standing feature. The moving features appear to emanate from the standing feature in a manner strikingly similar to the results of numerical two-dimensional relativistic magneto-hydrodynamic (RMHD) simulations in which moving shocks are generated at a recollimation shock (RCS). Because of this, and the close analogy to the jet feature HST-1 in M87, we identify the standing feature in BL Lac as an RCS. We assume that the magnetic field dominates the dynamics in the jet, and that the field is predominantly toroidal. From this we suggest that the moving features are compressions established by slow and fast mode magneto-acoustic MHD waves. We illustrate the situation with a simple model in which the slowest moving feature is a slow-mode wave, and the fastest feature is a fast-mode wave. In the model, the beam has Lorentz factor {Gamma}_beam_^gal^~3.5 in the frame of the host galaxy and the fast mode wave has Lorentz factor {Gamma}_Fwave_^beam^~1.6 in the frame of the beam. This gives a maximum apparent speed for the moving features, {beta}_app_=v_app_/c=10. In this model the Lorentz factor of the pattern in the galaxy frame is approximately three times larger than that of the beam itself.