  We present a morphological and spectral study of a sample of 99 BL Lacs using
the LOFAR Two-Metre Sky Survey Second Data Release (LDR2). Extended emission
has been identified at gigahertz frequencies around BL Lacs, but with LDR2 it
is now possible to systematically study their morphologies at 144 MHz, where
more diffuse emission is expected. LDR2 reveals the presence of extended radio
structures around 66/99 of the BL Lac nuclei, with angular extents ranging up
to 115 arcseconds, corresponding to spatial extents of 410 kpc. The extended
emission is likely to be both unbeamed diffuse emission and beamed emission
associated with relativistic bulk motion in jets. The spatial extents and
luminosities of the extended emission are consistent with the AGN unification
scheme where BL Lacs correspond to low-excitation radio galaxies with the jet
axis aligned along the line-of-sight. While extended emission is detected
around the majority of BL Lacs, the median 144-1400 MHz spectral index and core
dominance at 144 MHz indicate that the core component contributes ~42% on
average to the total low-frequency flux density. A stronger correlation was
found between the 144 MHz core flux density and the gamma-ray photon flux (r =
0.69) compared to the 144 MHz extended flux density and the gamma-ray photon
flux (r = 0.42). This suggests that the radio-to-gamma-ray connection weakens
at low radio frequencies because the population of particles that give rise to
the gamma-ray flux are distinct from the electrons producing the diffuse
synchrotron emission associated with spatially-extended features.
