We study the far-infrared properties of 498 Lyα emitters (LAEs) at z = 2.8, 3.1, and 4.5 in the Extended Chandra Deep Field-South, using 250, 350, and 500 μm data from the Herschel Multi-tiered Extragalactic Survey and 870 μm data from the LABOCA ECDFS Submillimeter Survey. None of the 126, 280, or 92 LAEs at z = 2.8, 3.1, and 4.5, respectively, are individually detected in the far-infrared data. We use stacking to probe the average emission to deeper flux limits, reaching 1σ depths of ~0.1 to 0.4 mJy. The LAEs are also undetected at >=3σ in the stacks, although a 2.5σ signal is observed at 870 μm for the z = 2.8 sources. We consider a wide range of far-infrared spectral energy distributions (SEDs), including an M82 and an Sd galaxy template, to determine upper limits on the far-infrared luminosities and far-infrared-derived star formation rates of the LAEs. These star formation rates are then combined with those inferred from the Lyα and UV emission to determine lower limits on the LAEs' Lyα escape fraction (f esc(Lyα)). For the Sd SED template, the inferred LAEs f esc(Lyα) are >~ 30% (1σ) at z = 2.8, 3.1, and 4.5, which are all significantly higher than the global f esc(Lyα) at these redshifts. Thus, if the LAEs f esc(Lyα) follows the global evolution, then they have warmer far-infrared SEDs than the Sd galaxy template. The average and M82 SEDs produce lower limits on the LAE f esc(Lyα) of ~10%-20% (1σ), all of which are slightly higher than the global evolution of f esc(Lyα), but consistent with it at the 2σ-3σ level.