  We examine the dependence of derived physical parameters of distant Lyman
break galaxies (LBGs) on the assumed star formation histories (SFHs), their
implications on the SFR-mass relation, and we propose observational tests to
better constrain these quantities. We use our SED-fitting tool including
nebular emission to analyze a large sample of LBGs, assuming five different
star formation histories, extending our first analysis of this sample (de
Barros et al. 2012, paper I). In addition we predict the IR luminosities
consistently with the SED fits.
  Compared to "standard" SED fits assuming constant SFR and neglecting nebular
lines, assuming variable SFHs yield systematically lower stellar masses, higher
extinction, higher SFR, higher IR luminosities, and a wider range of equivalent
widths for optical emission lines. Exponentially declining and delayed SFHs
yield basically identical results and generally fit best. Exponentially rising
SFHs yield similar masses, but somewhat higher extinction.
  We find significant deviations between the derived SFR and IR luminosity from
the commonly used SFR(IR) or SFR(IR+UV) calibration, due to differences in the
SFHs and ages. Models with variable SFHs, favored statistically, yield
generally a large scatter in the SFR-mass relation. We show that the true
scatter in the SFR-mass relation can be significantly larger than inferred
using SFR(UV) and/or SFR(IR).
  Different SFHs, and hence differences in the derived SFR-mass relation and in
the specific star formation rates, can be tested/constrained observationally
with future IR observations with ALMA. Measurement of emission lines, such as
Halpha and [OII]3727, can also provide useful constraints on the SED models. We
conclude that our findings of a large scatter in SFR-mass at high-z and an
increase of the specific star formation rate above z>~3 (paper I) can be tested
observationally. (abriged)
