  We make a systematic study of $\Lambda$ hyperon polarizations in unpolarized
lepton induced semi-inclusive reactions such as $e^-N\to e^-\Lambda X$ and
$e^+e^-\to\Lambda h X$. We present the general form of cross sections in terms
of structure functions obtained from a general kinematic analysis. This already
shows that the produced hyperons can be polarized in three orthogonal
directions, i.e., the longitudinal direction along the hyperon momentum, the
normal direction of the production plane, and the transverse direction in the
production plane. We present the parton model results at the leading twist and
leading order in perturbative QCD and provide the expressions for these
structure functions and polarizations in terms of parton distribution functions
and fragmentation functions. We emphasize in particular that by studying the
longitudinal polarization and the transverse polarization in the production
plane, we can extract the corresponding chiral-odd fragmentation functions
$H_{1Lq}^{\perp\Lambda}$, $H_{1Tq}^{\Lambda}$ and $H_{1Tq}^{\perp\Lambda}$. We
also present numerical results of rough estimates utilizing available
parameterizations of fragmentation functions and approximations. We discuss how
to measure these polarizations and point out in particular that they can be
carried out in future EIC and/or $e^+e^-$ annihilation experiments such as
Belle.
