The recently developed plasmonic and photonic metal-semiconductor nanolasers feature unique properties, such as ultra-small mode volume and footprint, high Purcell factor, and ultra-fast modulation. However, it is often difficult to recognize when the transition to lasing occurs, while the most important feature of laser radiation, i.e., coherence, is available only above the lasing threshold. Here we systematically study the second-order coherence properties of metal-semiconductor nanolasers at both low- and high-pump rates. We find the lasing threshold using a clear coherence definition and derive a simple expression for the threshold pump current (optical pump power), which can be applied to most thresholdless and non-thresholdless metal-semiconductor nanolasers.