We investigated ordering of the vortex lattice under the influence of a driving current in amorphous superconducting films of Nb70Ge30 with varying amounts of disorder. Using the nonlinear behavior of the voltage versus current relations, i.e., the peak in the dynamical resistance, we map the occurrence of this dynamical ordering (DO) in the (B,T) phase diagram. Using the collective pinning analysis, DO is shown to appear when the size of the correlated regions drops below the order of ~ ten times the vortex lattice distance. This means that for weaker intrinsic disorder, DO moves closer to the melting line. The current at which DO occurs diverges at the melting transition, in agreement with the notion that increasing velocities are needed to overcome the effect of either temperature or softening of the shear modulus of the vortex lattice.