In this paper, the concepts of LwH-sets and LwH-closed spaces are proposed in Lw-spaces by means of (aw)--remote neighborhood family. The characterizations of LwH-sets and LwH-closed spaces are systematically discussed. Some important properties of LwH-closed spaces, such as the LwH-closed spaces is w-regular closed hereditary, arbitrarily multiplicative and preserving invariance under almost ( w 1, w 2)-continuous mappings are proved.