The $^{176}$Lu-$^{176}$Hf nuclear decay is a powerful tool for measuring the age of astrophysical and geological events and has been used as a “cosmochronometer”. However, existing half-life values of $^{176}$Lu vary significantly. This paper reports half-life measurements using a windowless 4π solid angle detector based on bismuth germanate (BGO) scintillation crystals. A natural Lu sample is placed inside the detector, allowing for measurement of the total energy released from $^{176}$Lu decay. The measured half-life of (3.719 ± 0.007) × 10$^{10}$ yr is consistent with values obtained from terrestrial rocks.