Hf1-xLuxW2O8-y solid solutions up to x = 0.04, based on a negative thermal expansion material HfW2O8, were synthesized by a solid sate 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 WO4 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 WO4 pairs were estimated from the characteristic diffraction peak at sufficient low temperature. These behaviors of Hf1-xLuxW2O8-y are consistent with those of Zr1-xMxW2O8-y (M = Sc, Y, In, Lu). The drastic suppression of T-trs in Hf1-xLuxW2O8-y can be interpreted in the framework of a model proposed for Zr1-xMxW2O8-y, which states the existence of a local nanoregion including the WO4 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.