The local lattice structure in newly discovered LaFeAsO1-xFx superconductors is studied by extended x-ray absorption fine structure measurements. An anomalous upturn of the mean-square relative displacement of the Fe-As bond is detected below ~70 K as electron carriers are introduced,reflecting the occurrence of Fe-As bond local lattice fluctuation. Similar to that in cuprates, this lattice fluctuation exhibits an abrupt depression at the onset superconducting transition temperature. The results indicate that strong electron-lattice interaction is involved in the superconducting transition in oxypcnictide superconductors, putting a strict limitation on possible theoretical models.