Neutron production in lead by cosmic muons has been studied with a Gadolinium doped liquid scintillator detector. The detector was installed next to the Muon-Induced Neutron Indirect Detection EXperiment (MINIDEX), permanently located in the Tubingen shallow underground laboratory where the mean muon energy is approximately 7 GeV. The MINIDEX plastic scintillators were used to tag muons; the neutrons were detected through neutron capture and neutron-induced nuclear recoil signals in the liquid scintillator detector. Results on the rates of observed neutron captures and nuclear recoils are presented and compared to predictions from GEANT4-9.6 and GEANT4-10.3. The predicted rates are significantly too low for bo