  In its observation band, the Laser Interferometer Space Antenna (LISA) will
simultaneously observe stochastic gravitational-wave background (SGWB) signals
of different origins; orbitally modulated waveforms from galactic white dwarf
binaries, a binary black hole produced background, and possibly a
cosmologically produced SGWB. We simulate the emission of gravitational waves
from galactic white dwarf binaries based on the Lamberts \cite{Lamberts}
distributions and determine a complex waveform from the galactic foreground. We
generate the modulated galactic signal detected by LISA due to its orbital
motion, and present a data analysis strategy to address it. The Fisher
Information and Markov Chain Monte Carlo methods give an estimate of the LISA
noise and parameters for the different signal sources. We simultaneously
estimate the galactic foreground, the astrophysical and cosmological
backgrounds, and estimate detection limits for the future LISA observation of
the SGWB in the spectral domain with the 3 LISA channels $ A $, $ E $ and $ T
$. In the context of the expected astrophysical background and a galactic
foreground, a cosmological background energy density of about $
\Omega_{GW,Cosmo} \approx 8 \times 10^{-13} $ could be detected by LISA with
our spectral separation strategy.
