We propose a high-sensitivity magnetometry scheme based on a diamond Raman laser with visible pump absorption by an ensemble of coherently microwave driven negatively charged nitrogen-vacancy centres (NV) in the same diamond crystal. The NV centres absorption and emission are spin-dependent. We show how the varying absorption of the NV centres changes the Raman laser output. A shift in the diamond Raman laser threshold and output occurs with the external magnetic-field and microwave driving. We develop a theoretical framework including steady-state solutions to describe the effects of coherently driven NV centres in a diamond Raman laser. We discuss that such a laser working at the threshold can be employed for magnetic-field sensing. In contrast to previous studies on NV magnetometry with visible laser absorption, the laser threshold magnetometry method is expected to have low technical noise, due to low background light in the measurement signal. For magnetic-field sensing, we project a shot-noise limited DC sensitivity of a few $mathrm{pT}/sqrt{mathrm{Hz}}$ in a well-calibrated cavity with realistic parameters. This sensor employs the broad visible absorption of NV centres and unlike previous laser threshold magnetometry proposals it does not rely on active NV centre lasing or an infrared laser medium at the specific wavelength of the NV centres infrared absorption line.
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