The reported lifetime in an in-beam neutron lifetime experiment performed at NIST was tn = (886.3 ± 3.4) s. The largest source of uncertainty was the efficiency of the neutron flux monitor (0.3% relative uncertainty). The flux monitor operates by counting charged particles produced when neutrons impinge on a 6Li foil. Its efficiency was calculated from the 6Li thermal neutron cross section, the solid angle subtended by the charged particle detectors, and the amount of neutron-absorbing material present on the foil. An absolute black neutron detector for cold neutron beams has been developed to measure the efficiency without the need to know these quantities. The flux monitor efficiency is measured to a precision of 0.052% using this direct calibration technique. This calibration removes the largest barrier to a 1 s neutron lifetime measurement with the beam technique. It is hoped that this data can also be used to re-evaluate the current NIST neutron lifetime value, reduce its uncertainty, and remove the dependence on evaluated nuclear data files. There is also the possibility for a direct measurement of the 6Li thermal neutron cross section.