In this Letter, we have investigated experimentally the photonic realization of a moving lattice with an instantaneously tunable transverse velocity in a three-level Λ-type warm 85Rb atomic medium. The dynamic photonic lattice moving along the direction of its spatial periodicity was constructed by introducing a frequency difference (determining the velocity) between two coupling beams, whose interference pattern could optically induce a (spatial) periodic refractive index change inside the atomic vapor under electromagnetically induced transparency. When a Gaussian probe field is launched into this optically induced lattice, the output diffraction patterns can shift along the transverse direction, indicating dynamical features of induced photonic structures. The realization of this effectively controllable moving photonic lattice provides a new platform for guiding the transport of light.