  Leading $\Lambda$ (LL) production in $ep$ collisions at high energies is
investigated using the color dipole formalism and taking into account the
nonlinear QCD effects. In particular, the impact of the absorptive effects on
the LL spectra are estimated considering the kinematical range that will be
probed by the Electron Ion Collider (EIC) and by the Large Hadron electron
Collider (LHeC). Our results indicate that the LL spectrum is strongly
suppressed at small photon virtualities. These results suggest that absorptive
effects are not negligible and should be taken into account in order to extract
the kaon structure function from data on leading $\Lambda$ production.
