  (abridged) We present near-infrared Ks-band imaging of 13 high redshift (0.6
< z < 1.3) BL Lac objects. We clearly detect the host in eight objects, and
marginally in three others. In all cases, the host galaxy is well represented
by an r^1/4 surface brightness law. The host galaxies of high redshift BL Lacs
are large (<R(e)> ~7 kpc) and very luminous (<M(K)> = -27.9+-0.7), ~3 mag
brighter than L*, and ~1 mag brighter than brightest cluster galaxies. They are
also ~1 mag brighter than low redshift radio galaxies and appear to deviate
from their K-z relationship. On the other hand, the high luminosities agree
with the few optical studies of high redshift BL Lac hosts. The nuclear
luminosity and the nucleus-galaxy luminosity ratio of the high redshift BL Lacs
are much larger than those in low redshift BL Lacs. This may be due to either a
higher intrinsic nuclear luminosity, or enhanced luminosity because of strong
beaming. Contrary to what is observed in low redshift BL Lacs, the luminosities
of the host galaxy and of the nucleus are fairly well correlated, as expected
from the black hole mass - bulge luminosity relationship. High redshift BL Lacs
radiate with a wide range of power with respect to their Eddington luminosity,
and this power is intermediate between those in nearby BL Lacs and in luminous
radio-loud quasars. The high redshift BL Lac host galaxies appear to be ~2 mag
brighter than those at low redshift. This is likely due to a strong selection
effect in the surveys of BL Lacs that makes observable only the most luminous
sources at z > 0.5 and produces a correlation between the nuclear and the host
luminosity. However, this may also suggest strong luminosity evolution which is
inconsistent with a simple passive evolution of the host galaxies, and requires
a contribution from relatively recent star formation episodes.
