The Lockman Hole is a well-studied extragalactic field with extensive multi-band ancillary data covering a wide range in frequency, essential for characterizing 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 18.6x14.7-arcsec and reaches an rms of 160{mu}Jy/beam 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+/-0.015. 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_ ~10mJy 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 150MHz. Using the deep, multi-frequency data available in the Lockman Hole, we identify a sample of 100 ultra-steep-spectrum sources and 13 peaked-spectrum sources. We estimate that up to 21 per cent 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.