In this paper, we suggest that semi-inclusive Lambda production with a
high energy electron or muon beam may be employed as an effective way
to pin down the possible importance of the generalized Sullivan proce
ss, in which the virtual photon may strike and smash the meson in the
cloud surrounding the target proton. The role of such generalized Sull
ivan processes in deep inelastic scattering (DIS) has been exploited r
ecently in connection with the observed violation of the Gottfried sum
rule as well as with the so-called ''proton spin crisis''. Our presen
t numerical results indicate that, in the kinematic region characteriz
ed typically by small x, large z, and a small specific range of y (wit
h the parton variables z, y, and z defined in the standard manner), th
e contribution from Sullivan processes may indeed be of numerical impo
rtance as compared to that due to the fragmentation process.