  The general Minimal Supersymmetric Standard Model introduces new sources for
Lepton Flavor Violation (LFV) as well as CP-violation. In this paper, we show
that when both sources are present, the electric dipole moment of the electron,
$d_e$, receives a contribution from the phase of the trilinear $A$-term of
staus, $\phi_{A_\tau}$. For $\phi_{A_\tau}=\pi/2$, the value of $d_e$,
depending on the ratios of the LFV mass elements, can range between zero and
three orders of magnitude above the present bound. We show that the present
bound on $d_e$ rules out a large portion of the CP-violating and the LFV
parameter space which is consistent with the bounds on the LFV rare decays.
  We show that studying the correlation between $d_e$ and the P-odd asymmetry
in $\tau \to e\gamma$ helps us to derive a more conclusive bound on
$\phi_{A_\tau}$
  We also discuss the possibility of cancelation among the contributions of
different CP-violating phases to $d_e$.
