  We analyze experimental data for the production of Lambda baryons in e^+e^-
annihilation in terms of scale dependent, QCD evolved, Lambda fragmentation
functions. Apart from the vast majority of the data for which the polarization
of an observed Lambda was not determined, we also consider the recent LEP
measurements of the longitudinal polarization of Lambda's produced on the
Z-resonance. Such data correspond to spin-dependent fragmentation functions for
the Lambda. We point out that the present data are insufficient to
satisfactorily fix these. We therefore suggest several different sets of
fragmentation functions, all compatible with present data, and study the
prospects for conceivable future semi-inclusive deep-inelastic scattering
experiments to discriminate between them. We provide the complete
next-to-leading order QCD framework for all the processes we consider.
