  The hydrogen Lyman-$\alpha$ (H {\sc i} Ly$\alpha$) emission during solar
flares has rarely been studied in spatially resolved images and its physical
origin has not been fully understood. In this paper, we present novel
Ly$\alpha$ images for a C1.4 solar flare (SOL2021-08-20T22:00) from the Extreme
Ultraviolet Imager aboard Solar Orbiter, together with multi-waveband and
multi-perspective observations from the Solar Terrestrial Relations Observatory
Ahead and the Solar Dynamics Observatory spacecraft. It is found that the
Ly$\alpha$ emission has a good temporal correlation with the thermal emissions
at 1--8 \AA\ and 5--7 keV, indicating that the flaring Ly$\alpha$ is mainly
produced by a thermal process in this small event. However, nonthermal
electrons play a minor role in generating Ly$\alpha$ at flare ribbons during
the rise phase of the flare, as revealed by the hard X-ray imaging and spectral
fitting. Besides originating from flare ribbons, the Ly$\alpha$ emission can
come from flare loops, likely caused by plasma heating and also cooling that
happen in different flare phases. It is also found that the Ly$\alpha$ emission
shows fairly similar features with the He {\sc ii} 304 \AA\ emission in light
curve and spatio-temporal variation along with small differences. These
observational results improve our understanding of the Ly$\alpha$ emission in
solar flares and also provide some insights for investigating the Ly$\alpha$
emission in stellar flares.
