Aims. This work explores from a statistical point of view the rest-frame far-ultraviolet (FUV) to far-infrared (FIR) emission of a population of Lyman break galaxies (LBGs) at z ∼ 3 that cannot be individually detected from current FIR observations. Methods. We perform a stacking analysis over a sample of ∼17000 LBGs at redshift 2.5 < z < 3.5 in the COSMOS field. The sample is binned as a function of UV luminosity (L FUV ), UV continuum slope (β UV ), and stellar mass (M * ), and then, stacked at optical (BVriz bands), near-infrared (Y JHK s bands), IRAC (3.6, 4.5, 5.6 and 8.0 µm), MIPS (24µm), PACS (100 and 160 µm), SPIRE (250, 350, and 500 µm), and AzTEC (1.1mm) observations. We obtain thirty rest-frame FUV-to-FIR spectral energy distribution (SEDs) of LBGs at z ∼ 3, and analyze them with CIGALE SED-fitting analysis code. We are able to derive fully consistent physical parameters (M * , β UV , L FUV , L IR , A FUV , SFR, and slope of the dust attenuation law), and build a semi-empirical library of thirty rest-frame FUV-to-FIR stacked LBG SEDs as a function of L FUV , β UV , and M * . Results. We used the so-called IR-excess (IRX ≡ L IR /L FUV ) to investigate the dust attenuation as a function of β UV and M * . Our LBGs, averaged as a function of β UV , follow the well known IRX-β UV calibration of local starburst galaxies. They, stacked as a function of M * , are in agreement with previous IRX-M * relationship presented on the literature at high M * (log(M * [M ])> 10). However, a large dispersion is shown in the IRX-β UV and IRX-M * planes, when the β UV and M * are combined to average the sample. Additionally, the SED-fitting analysis results provide a diversity of dust attenuation curve along the LBG sample, and their slope are well correlated with M * . Stepper dust attenuations curves than Calzetti's are favoured in low stellar mass LBGs (log(M * [M ]) < 10.25), while grayer ones are favoured in high stellar mass LBGs (log(M * [M ]) > 10.25). We also demonstrate that the slope of the dust attenuation curves is one of the main drivers to shape the IRX-β UV plane.