Hf(1-x)Lu(x)W(2)O(8-y) solid solutions up to x = 0.04, based on a negative thermal expansion material HfW(2)O(8), were synthesized by a solid state reaction method. X-ray diffraction experiments of these solid solutions from 90 to 560 K indicated thermal contraction with increasing temperature. Temperatures of order-disorder phase transition (T(trs)) associated with the orientation of WO(4) tetrahedra were determined from disappearance of a characteristic diffraction peak (310). The T(trs) of the solid solutions drastically decreased with increasing Lu content. Saturated order parameters (eta(s)) associated with the orientational order of the WO(4) pairs were estimated from the characteristic diffraction peak at sufficient low temperature. These behaviors of Hf(1-x)Lu(x)W(2)O(8-y) are consistent with those of Zr(1-x)M(x)W(2)O(8-y) (M = Sc, Y, In, Lu). The drastic suppression of T(trs) in Hf(1-x)Lu(x)W(2)O(8-y) can be interpreted in the framework of a model proposed for Zr(1-x)M(x)W(2)O(8-y), which states the existence of a local nanoregion including the WO(4) pairs having the frozen-in orientational disorder. To understand the substitution effect on the order-disorder phase transition comprehensively, classification based on the saturated order parameter eta(s) of the phase transition of AW(2)O(8) (A = Hf, Zr)-based solid solutions was carried out and discussed.