The SKA era is set to revolutionize our understanding of neutral hydrogen (HI) in individual galaxies out to redshifts of z~0.8; and in the z > 6 intergalactic medium through the detection and imaging of cosmic reionization. Direct HI number density constraints will, nonetheless, remain relatively weak out to cosmic noon (z~2) - the epoch of peak star formation and black hole accretion - and beyond. However, as was demonstrated from the 1990s with molecular line observations, this can be overcome by utilising the natural amplification afforded by strong gravitational lensing, which results in an effective increase in integration time by the square of the total magnification (\mu^2) for an unresolved source. Here we outline how a dedicated lensed HI survey will leverage MeerKAT's high sensitivity, frequency coverage, large instantaneous bandwidth, and high dynamic range imaging to enable a lasting legacy of high-redshift HI emission detections well into the SKA era. This survey will not only provide high-impact, rapid-turnaround MeerKAT science commissioning results, but also unveil Milky Way-like systems towards cosmic noon which is not possible with any other SKA precursors/pathfinders. An ambitious lensed HI survey will therefore make a significant impact from MeerKAT commissioning all the way through to the full SKA era, and provide a more complete picture of the HI history of the Universe.