The Lyman-alpha (Ly $\alpha $ ; 1216 Å) line is the brightest emission line in the quiescent solar spectrum and radiates a significant fraction of the available nonthermal energy during flares. Despite its importance, there is a lack of detailed studies of Ly $\alpha $ spectral variability during flares. Recently, spectrally resolved Ly $\alpha $ flare observations from the SORCE/SOLSTICE instrument have become available. This study examines Ly $\alpha $ spectral variability and its relationship with HXR emission from nonthermal electrons, using observations of two M-class flares from SORCE/SOLSTICE and RHESSI. Imaging observations from STEREO/SECCHI EUVI and SDO/AIA provide further context. Enhancements across the Ly $\alpha $ line profile were found to closely correlate with bursts of HXR emission, suggesting a primarily nonthermal origin. Red enhancement asymmetries at the peak of each flare were attributed to chromospheric evaporation, while blue wing enhancement and blue asymmetry were linked to a bright filament-eruption seen in SDO/AIA 1600 Å images. These findings contribute to the understanding of spectral Ly $\alpha $ variability during flares and highlight the need for future studies using a higher quality and quantity of spectral Ly $\alpha $ flare observations. Such studies will further characterise the physical mechanisms driving Ly $\alpha $ flare variability.