The orientation and deformation of moving vortex lattices in the flux-flow state have been investigated in amorphous superconducting NbGe thin films. Employing a mode-locking technique, we detect how moving lattices deform and their orientation changes as a magnetic field is tilted from normal to the film surface. For high tilt angles the lattice orientation is aligned parallely with the tilt direction. Meanwhile for low tilt angles the lattice orientation depends on the vortex velocity and a velocity-induced reorientation occurs. The characteristic velocity for the reorientation varies remarkably as the moving lattices deform. The observed features are consistent with an extended bond-fluctuation theory, revealing that the anisotropic shaking vortex motion is essential for determining the orientation of moving vortex lattices.