Spin relaxation was studied in a two-dimensional electron gas confined in a wide GaAs quantum well. Recently, the control of the spin relaxation anisotropy by diffusive motion was first shown in D. Iizasa et al., arXiv:2006.08253. Here, we demonstrate electrical control by drift transport in a system with two subbands occupied. The combined effect of in-plane and gate voltages was investigated using time-resolved Kerr rotation. The measured relaxation time presents strong anisotropy with respect to the transport direction. For an in-plane accelerating electric field along 110, the lifetime was strongly suppressed irrespective of the applied gate voltage. Remarkably, for transport along 11¯0, the data shows spin lifetime that was gate dependent and longer than in the 110 direction regardless of the in-plane voltage. In agreement, independent results of anisotropic spin precession frequencies are also presented. Nevertheless, the long spin lifetime, strong anisotropy and drift response seen in the data are beyond the existing models for spin drift and diffusion.