We investigate the transverse target spin asymmetry $A^{sinphi_{S}}_{UT}$ 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 $sinphi_{S}$ 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.
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