The study of the extended emission and polarization properties of BL Lacs is an important step for the identification of their parent population. FRI radio sources, the supposed parent population of BL Lacs, have weaker extended radio luminosity and a dominant inferred magnetic field perpendicular to the jet, while FRII radio sources, the supposed parent population of quasars, have stronger extended radio power and an inferred magnetic field parallel to the jet. The only complete sample of radio selected BL Lacs (1 Jy sample, Stickel et al. 1991, ApJ, 374, 431) contains 34 objects. Unfortunately, about half of 1 Jy BL Lacs do not have very high dynamic range images, necessary to detect the low emissivity radio emission surrounding the bright compact source, either because the object was never observed, or because the observation was carried out at the beginning of 1980s with low sensitivity. In 1994 we started a programme using the VLA (A, B, and D configuration, see Table 1) and the WSRT (W in Table 1) to complete the high sensitivity radio imaging of the 1 Jy sample. We aim to investigate morphology and polarization properties, as well as the luminosity of the extended emission. This contribution presents the L band observations. The results are very preliminary, some of the data reduction is still in progress as well as the statistical analysis. The sources in Table 1 have been roughly classified as extended (E), or point-like (P) if no extended feature was detected. Among the 15 sources observed at the highest resolution 13 were classified as extended. In many sources we detect significantly much more extended flux than previously reported from earlier observations. Almost all the BL Lac objects we observed at the highest resolution show some extended features; furthermore, in a few cases, we detected emission on the arcminute scale. The power of the extended luminosity covers 3 orders of magnitude, 3 objects (0537–441, 0820+225, and 2240–260) have values typical of a FRII radio source. These new data will be used for an updated statistical analysis of the properties of the extended emission in the 1 Jy sample of BL Lac objects.