Lyman break Galaxies are galaxies selected in the rest-frame ultraviolet. But, one important and missing information for these Lyman break galaxies is the amount of dust attenuation. This is crucial to estimate the total star formation rate of this class of objects and, ultimately, the cosmic star formation density. AKARI, Spitzer and Herschel are therefore the major facilities that could provide us with this information. As part of the Herschel Multi-tiered Extragalactic Survey, we have began investigating the rest-frame far-infrared properties of a sample of more than 4,800 Lyman Break Galaxies in the GOODS-North fiels. Most LBGs are not detected individually, but we do detect a sub-sample of 12 objects at 0.7 < z <1.6 and one object at z = 2.0. The ones detected by Herschel SPIRE have redder observed NUV-U and U-R colors than the others, while the undetected ones have colors consistent with average LBGs at z > 2.5. We have analysed their UV-to-FIR spectral energy distributions using the code cigale to estimate their physical parameters. We find that LBGs detected by SPIRE are high mass, luminous infrared galaxies. They also appear to be located in a triangle-shaped region in the AFUV vs. logLFUV diagram limited by AFUV = 0 at the bottom and by a diagonal following the temporal evolution of the most massive galaxies from the bottom-right to the top-left of the diagram. In a second step, we move to the larger COSMOS field where we have been able to detect 80 Lyman break galaxies (out of ~ 15,600) in the far infrared. They form the largest sample of Lyman break galaxies at z > 2.5 detected in the far-infrared. We tentatively name them Submillimeter Lyman break galaxies (S-LBGs).