Calculations are presented for the space density of BL Lac objects having extended emission with luminosity greater than or equal to 10 to the 22nd W/Hz sr at 1.4 GHz. These results are then compared with the space density of elliptical radio galaxies with the same luminosity. It is proposed that, if the characteristic properties of BL Lacs are a result of relativistic beaming, then elliptical radio galaxies are the unaligned parent population of the BL Lac objects. The relative space densities are found to constrain the Lorentz factor of the beams in BL Lacs (and radio galaxies) to be less than or approximately equal to 5.4. Lorentz factors of greater than or approximately equal to 4 are shown to be sufficient to boost the weak central component of an elliptical radio galaxy into the dominant core of a BL Lac object.