  The stacked spectral energy distribution (SED) of Multiband Imaging
Photometer for Spitzer (MIPS) 24$\mu m$ detected Lyman break galaxies
(MIPS-LBGs) is fitted by means of spectro-photometric model GRASIL with an
"educated" fitting approach which benefits from results of chemical evolution
models. The star formation rate(SFR)-age-metallicity degeneracies of SED
modelling are broken by using SFH and chemical enrichment history suggested by
chemical models, which also provide dust mass, dust abundance and chemical
elements locked in dust component. We derive the total mass $M_{tot}$, stellar
mass $M_{\ast}$, gas mass $M_{g}$, dust mass $M_{d}$, age and SFR of the
stacked MIPS-LBG in a self-consistent way. Our estimate of $M_{\ast}= 8\times
10^{10}$ agrees with other works based on UV-optical SED fitting. We suggest
that MIPS-LBGs at $z\sim3$ are young (0.3-0.6 Gyr), massive ($M_{tot} \sim
10^{11} M_{\odot}$), dusty ($M_{d} \sim 10^{8} M_{\odot}$), metal rich ($Z \sim
Z_{\odot} $) progenitors of elliptical galaxies suffering a strong burst of
star formation (SFR $\sim 200 M_{\odot}/yr$). Our estimate of $M_{d}=7 \times
10^{7} M_{\odot}$ of the stacked MIPS-LBG is about a factor of eight lower than
the estimated value based on single temperature grey-body fitting, suggesting
that self-consistent SED models are needed to estimate dust mass. By comparing
with the Milky Way molecular cloud and dust properties, we suggest that denser
and dustier environments and flatter dust size distribution are likely in high
redshift massive star forming galaxies. These dust properties, as well as the
different types of SFHs, can cause different SED shapes between high redshift
star-forming ellipticals and local star-burst templates. This discrepancy of
SED shapes could in turn explain the non detection at submillimeter
wavelengths, of IR luminous ($L_{IR} \succeq 10^{12} L_{\odot} $) MIPS-LBGs.
