  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 $z\sim3$ that cannot be individually detected from
current FIR observations. We perform a stacking analysis over a sample of
$\sim$17000 LBGs at redshift $2.5<z<3.5$ in the COSMOS field. The sample is
binned as a function of UV luminosity ($L_{\mathrm{FUV}}$), UV continuum slope
($\beta_{\mathrm{UV}}$), and stellar mass (M$_{*}$), and then, stacked at
optical ($BVriz$ bands), near-infrared ($YJHKs$ bands), IRAC (3.6, 4.5, 5.6 and
8.0 $\mu$m), MIPS (24$\mu$m), PACS (100 and 160~$\mu$m), SPIRE (250, 350, and
500~$\mu$m), and AzTEC (1.1mm) observations. We obtain thirty rest-frame
FUV-to-FIR spectral energy distribution (SEDs) of LBGs at $z\sim3$, and analyse
them with CIGALE SED-fitting analysis code. We are able to derive fully
consistent physical parameters (M$_{*}$, $\beta_{\mathrm{UV}}$,
$L_{\mathrm{FUV}}$, $L_{\mathrm{IR}}$, 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 $L_{\mathrm{FUV}}$,
$\beta_{\mathrm{UV}}$, and M$_{*}$. We used the so-called IR-excess ($IRX
\equiv L_{\mathrm{IR}} / L_{\mathrm{FUV}}$) to investigate the dust attenuation
as a function of $\beta_{\mathrm{UV}}$ and M$_{*}$. 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
($\log(M_{*} [M_{\odot}]) < 10.25$), while grayer ones are favoured in high
stellar mass LBGs ($\log(M_{*} [M_{\odot}]) > 10.25$).
