  We present the results of a new study investigating the relationship between
observed Ly$\alpha$ equivalent width ($W_{\lambda}$(Ly$\alpha$)) and the
metallicity of the ionizing stellar population ($Z_{\star}$) for a sample of
$768$ star-forming galaxies at $3 \leq z \leq 5$ drawn from the VANDELS survey.
Dividing our sample into quartiles of rest-frame $W_{\lambda}$(Ly$\alpha$)
across the range $-58 \unicode{xC5} \lesssim$ $W_{\lambda}$(Ly$\alpha$)
$\lesssim 110 \unicode{xC5}$ we determine $Z_{\star}$ from full spectral
fitting of composite far-ultraviolet (FUV) spectra and find a clear
anti-correlation between $W_{\lambda}$(Ly$\alpha$) and $Z_{\star}$. Our results
indicate that $Z_{\star}$ decreases by a factor $\gtrsim 3$ between the lowest
$W_{\lambda}$(Ly$\alpha$) quartile
($\langle$$W_{\lambda}$(Ly$\alpha$)$\rangle=-18\unicode{xC5}$) and the highest
$W_{\lambda}$(Ly$\alpha$) quartile
($\langle$$W_{\lambda}$(Ly$\alpha$)$\rangle=24\unicode{xC5}$). Similarly,
galaxies typically defined as Lyman Alpha Emitters (LAEs;
$W_{\lambda}$(Ly$\alpha$) $>20\unicode{xC5}$) are, on average, metal poor with
respect to the non-LAE galaxy population ($W_{\lambda}$(Ly$\alpha$)
$\leq20\unicode{xC5}$) with $Z_{\star}$$_{\rm{non-LAE}}\gtrsim 2 \times$
$Z_{\star}$$_{\rm{LAE}}$. Finally, based on the best-fitting stellar models, we
estimate that the increasing strength of the stellar ionizing spectrum towards
lower $Z_{\star}$ is responsible for $\simeq 15-25\%$ of the observed variation
in $W_{\lambda}$(Ly$\alpha$) across our sample, with the remaining contribution
($\simeq 75-85\%$) being due to a decrease in the HI/dust covering fractions in
low $Z_{\star}$ galaxies.
