Neutron experiment is carried out on relaxor magnet LuFeCoO4 to study the coupling between the slow dynamics of the dielectric and magnetic properties. At 190 K, the nuclear and magnetic diffuse intensities change simultaneously. Furthermore, the magnetic correlation length along (1,1,0) direction coincides the size of the polar nanoregions estimated from nuclear diffuse scattering in the c-plane. Since the same domain provides both electric and magnetic properties, strong coupling between the two properties through the domain size is expected.