  The Lockman Hole is a well-studied extragalactic field with extensive
multi-band ancillary data covering a wide range in frequency, essential for
characterising the physical and evolutionary properties of the various source
populations detected in deep radio fields (mainly star-forming galaxies and
AGNs). In this paper we present new 150-MHz observations carried out with the
LOw Frequency ARray (LOFAR), allowing us to explore a new spectral window for
the faint radio source population. This 150-MHz image covers an area of 34.7
square degrees with a resolution of 18.6$\times$14.7 arcsec and reaches an rms
of 160 $\mu$Jy beam$^{-1}$ at the centre of the field.
  As expected for a low-frequency selected sample, the vast majority of sources
exhibit steep spectra, with a median spectral index of
$\alpha_{150}^{1400}=-0.78\pm0.015$. The median spectral index becomes slightly
flatter (increasing from $\alpha_{150}^{1400}=-0.84$ to
$\alpha_{150}^{1400}=-0.75$) with decreasing flux density down to $S_{150}
\sim$10 mJy before flattening out and remaining constant below this flux level.
For a bright subset of the 150-MHz selected sample we can trace the spectral
properties down to lower frequencies using 60-MHz LOFAR observations, finding
tentative evidence for sources to become flatter in spectrum between 60 and 150
MHz. Using the deep, multi-frequency data available in the Lockman Hole, we
identify a sample of 100 Ultra-steep spectrum (USS) sources and 13 peaked
spectrum sources. We estimate that up to 21 percent of these could have $z>4$
and are candidate high-$z$ radio galaxies, but further follow-up observations
are required to confirm the physical nature of these objects.
