  Measurements of transverse polarization of Lambda hyperons produced in high
energy pp collisions may help to address several open issues about Lambda
production and polarization mechanisms, such as the amount of SU(3) breaking,
the importance of gluons and sea quarks, and the origin of spontaneous Lambda
polarization. The process p + p -> Lambda^\uparrow + jet + X at midrapidity is
ideally suited for this purpose, for instance at LHC's ALICE experiment. New
expressions and predictions are presented for the transverse Lambda
polarization in this process, within a factorized description which involves
transverse momentum and spin dependence in the fragmentation process.
Uncertainties from the unpolarized Lambda fragmentation functions, due to the
unknown magnitude of SU(3) breaking and the apparent inconsistency between pp
and e^+ e^- data, are investigated.
