We have succeeded in synthesizing single-phase polycrystalline samples of oxygen-deficient oxypnictide superconductors, LnFeAsO 1Ày (Ln: lanthanide elements) with Ln ¼ La, Ce, Pr, Nd, Sm, Gd, Tb, and Dy using high-pressure technique. It is found out that the synthesis pressure is a key parameter for synthesizing samples, in particular for the heavier Ln's, such as Tb and Dy. The lattice parameters systematically decrease with the atomic number of Ln, reflecting the shrinkage of Ln ionic radius. For the lighter Ln's (La, Ce, Pr, Nd), T c increases monotonously with decreasing the lattice parameters from 26 K for Ln ¼ La to 54 K for Ln ¼ Nd, then stays at the constant value around 53 K for the heavier counterpart (Nd, Sm, Gd, Tb, and Dy). The results suggest the intimate relationship between the crystal structural parameters and the superconductivity, as well as the possible existence of the inherent maximum T c , which is located around 50 K in the LnFeAsO based materials.