  The LOFAR Two-metre Sky Survey (LoTSS) is a sensitive, high-resolution
120-168 MHz survey of the Northern sky. The LoTSS First Data Release (DR1)
presents 424 square degrees of radio continuum observations over the HETDEX
Spring Field (10h45m00s $<$ right ascension $<$ 15h30m00s and
45$^\circ$00$'$00$'$ $<$ declination $<$ 57$^\circ$00$'$00$''$) with a median
sensitivity of 71$\mu$Jy/beam and a resolution of 6$''$. In this paper we
present photometric redshifts (photo-$z$) for 94.4% of optical sources over
this region that are detected in the Panoramic Survey Telescope and Rapid
Response System (Pan-STARRS) 3$\pi$ steradian survey. Combining the Pan-STARRS
optical data with mid-infrared photometry from the Wide-field Infrared Survey
Explorer, we estimate photo-$z$s using a novel hybrid photometric redshift
methodology optimised to produce the best possible performance for the diverse
sample of radio continuum selected sources. For the radio-continuum detected
population, we find an overall scatter in the photo-$z$ of 3.9% and an outlier
fraction ($\left | z_{\rm{phot}} - z_{\rm{spec}} \right | / (1+z_{\rm{spec}}) >
0.15$) of 7.9%. We also find that, at a given redshift, there is no strong
trend in photo-$z$ quality as a function of radio luminosity. However there are
strong trends as a function of redshift for a given radio luminosity, a result
of selection effects in the spectroscopic sample and/or intrinsic evolution
within the radio source population. Additionally, for the sample of sources in
the LoTSS First Data Release with optical counterparts, we present rest-frame
optical and mid-infrared magnitudes based on template fits to the consensus
photometric (or spectroscopic when available) redshift.
