Experimental x-ray spectra of the H-like 2p --> 1s (Lyman-alpha) doublet have been obtained using time-integrated high-resolution spectroscopy of a constrained-flow, laser-generated aluminum plasma. These spectra show monotonic alteration of the relative intensities of the doublet components with distance from the target surface. Excellent agreement between experiment and theory is found only if the modeling includes both ion collisional rates between the fine-structure components of the level and, more importantly, the radiative pumping of one Lyman-alpha component by the other component along the direction of the major velocity gradient (i.e., perpendicular to the direction of spectra observation). Understanding radiation transfer in plasmas with high velocity gradients is important in modeling many astrophysical objects, and this experiment acts as a benchmark for such complex calculations.