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We study the far-infrared properties of 498 Lyman Alpha Emitters (LAEs) atz=2.8, 3.1 and 4.5 in the Extended Chandra Deep Field-South, using 250, 350 and500 micron data from the Herschel Multi-tiered Extragalactic Survey (HerMES)and 870 micron data from the LABOCA ECDFS Submillimeter Survey (LESS). None ofthe 126, 280 or 92 LAEs at z=2.8, 3.1 and 4.5, respectively, are individuallydetected in the far-infrared data. We use stacking to probe the averageemission to deeper flux limits, reaching $1\sigma$ depths of ~0.1 to 0.4 mJy.The LAEs are also undetected at $\ge3\sigma$ in the stacks, although a$2.5\sigma$ signal is observed at 870 micron for the z=2.8 sources. We considera wide range of far-infrared spectral energy distributions (SEDs), including aM82 and an Sd galaxy template, to determine upper limits on the far-infraredluminosities and far-infrared-derived star-formation rates of the LAEs. Thesestar-formation rates are then combined with those inferred from the Ly$\alpha$and UV emission to determine lower limits on the LAEs Ly$\alpha$ escapefraction ($f_{\rm esc}($Ly$\alpha$)). For the Sd SED template, the inferredLAEs $f_{\rm esc}($Ly$\alpha$) are $\gtrsim30%$ ($1\sigma$) at z=2.8, 3.1 and4.5, which are all significantly higher than the global $f_{\rmesc}($Ly$\alpha$) at these redshifts. Thus, if the LAEs $f_{\rmesc}($Ly$\alpha$) follows the global evolution then they have warmerfar-infrared SEDs than the Sd galaxy template. The average and M82 SEDs producelower limits on the LAE $f_{\rm esc}($Ly$\alpha$) of ~10 to 20% ($1\sigma$),all of which are slightly higher than the global evolution of $f_{\rmesc}($Ly$\alpha$) but consistent with it at the 2 to 3$\sigma$ level.

Constraining the Lyman Alpha Escape Fraction with Far-Infrared Observations of Lyman Alpha Emitters