  We study the production of longitudinally polarized Lambda-baryons in
single-spin pp collisions at RHIC and HERA-N as a means of determining the
spin-dependent Lambda fragmentation functions. It is shown that a measurement
of the rapidity distribution of the Lambda's would provide an excellent way of
clearly discriminating between various recently suggested sets of polarized
Lambda fragmentation functions that are all compatible with present e^+e^-
data. We also address the main theoretical uncertainties, which appear to be
well under control.
