  We investigate the transverse target spin asymmetry $A^{\sin\phi_{S}}_{UT}$
for the unpolarized $\Lambda$ production in semi-inclusive deep inelastic
scattering with the transverse momentum of the final-state lambda hyperon being
integrated out. The asymmetry is contributed by the product of the transversity
distribution function $h_1(x)$ of the nucleon and the collinear twist-3
fragmentation function $\tilde{H}(z)$ of the $\Lambda$ hyperon. The later one
originates from the quark-gluon-quark correlation and is a naive
time-reversal-odd function. We calculate $\tilde{H}$ of the $\Lambda$ hyperon
by adopt a diquark spectator model. Using the numerical result of
$\tilde{H}(z)$ and the available parametrization of $h_1(x)$ from SIDIS data,
we predict the $\sin\phi_{S}$ asymmetry in the electroproduction of the
$\Lambda$ hyperon in the kinematical region of EIC, EicC and COMPASS. In the
phenomenological analysis we include the evolution effect of the distribution
functions and the fragmentation functions. The results show that the
asymmetries for the $\Lambda$ production SIDIS process is around 0.1 and may be
accessible at EIC, EicC and COMPASS. We also find that the evolution of
fragmentation function can affect the size of asymmetry.
