We investigated the microscopic magnetic state of the itinerant-electron ferromagnet LuInCo4 with a cobalt pyrochlore lattice by means of powder and single-crystal neutron diffraction measurements. The powder neutron diffraction profiles at zero field are well described by a simple q = 0 collinear ferromagnetic structure with an ordered Co moment of 0.9 uB. Single-crystal neutron diffraction experiments further suggest the absence of both antiferromagnetic order and long-period helical magnetic modulation. In addition, diffuse magnetic scattering was observed around q = 0, with its intensity distribution gradually broadened in reciprocal space upon cooling. Based on these observations, we propose a possible microscopic origin of the low-temperature metamagnetic transition in terms of a ferromagnetic instability enhanced by gradual localization of the itinerant Co-3d electrons. These results suggest that LuInCo4 provides a model system for investigating the interplay between electron localization and itinerant-electron ferromagnetism in cobalt-based metallic pyrochlore compounds.