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Spectroscopic observations of massive $z>7$ galaxies selected to haveextremely large [OIII]+H$\beta$ equivalent width (EW $\sim1500$ \r{A}) haverecently revealed large Ly$\alpha$ detection rates, in contrast to the weakemission seen in the general population. Why these systems are uniquely visiblein Ly$\alpha$ at redshifts where the IGM is likely significantly neutral is notclear. With the goal of better understanding these results, we have begun acampaign with MMT and Magellan to measure Ly$\alpha$ in galaxies with similar[OIII]+H$\beta$ EWs at $z\simeq2-3$. At these redshifts, the IGM is highlyionized, allowing us to clearly disentangle how the Ly$\alpha$ propertiesdepend on the [OIII]+H$\beta$ EW. Here we present Ly$\alpha$ EWs of $49$galaxies at $z=2.2-3.7$ with intense [OIII]+H$\beta$ line emission (EW$=300-3000$ \r{A}). Our results demonstrate that strong Ly$\alpha$ emission (EW$>20$ \r{A}) becomes more common in galaxies with larger [OIII]+H$\beta$ EW,reflecting a combination of increasingly efficient ionizing photon productionand enhanced transmission of Ly$\alpha$. Among the galaxies with the mostextreme [OIII]+H$\beta$ emission (EW $\sim1500$ \r{A}), we find that strongLy$\alpha$ emission is not ubiquitous, with only $50$ per cent of ourpopulation showing Ly$\alpha$ EW $>20$ \r{A}. Our data suggest that the rangeof Ly$\alpha$ strengths is related to the observed ellipticity, with thosesystems that appear edge-on or elongated having weaker Ly$\alpha$ emission. Weuse these results to interpret the anomalous Ly$\alpha$ properties seen in$z>7$ galaxies with extreme [OIII]+H$\beta$ emission and discuss implicationsfor the escape of ionizing radiation from these extreme line emitting galaxies.

Lyman-alpha spectroscopy of extreme [OIII] emitting galaxies at $z\simeq2-3$: Implications for Ly$\alpha$ visibility and LyC leakage at $z>6$