We present results from the measurement of the neutron production rate in lead by high energy cosmic-ray muons at a depth of 2850 m water equivalent (mean muon energy of 260 GeV). A tonne-scale highly segmented plastic scintillator detector was utilised to detect both the energy depositions from the traversing muons as well as the delayed radiative capture signals of the induced neutrons. Complementary Monte Carlo simulations reproduce well the distributions of muons and detected muon-induced neutrons. Absolute agreement between simulation and data is of the order of 25%. By comparing the measured and simulated neutron capture rates a neutron yield in pure lead of (5.78-0.28 +0.21)×10-3 neutrons/muon/(g/cm2) has been obtained.