The previous Faddeev calculation of the two-alpha plus Lambda system for 9 Lambda Be is extended to incorporate the spin-orbit components of the SU_6 quark-model baryon-baryon interactions. We employ the Born kernel of the quark-model Lambda N LS interaction, and generate the spin-orbit component of the Lambda alpha potential by the alpha-cluster folding. The Faddeev calculation in the jj-coupling scheme implies that the direct use of the quark-model Born kernel for the Lambda N LS component is not good enough to reproduce the small experimental value Delta E^exp_{ls}=43 +- 5 keV for the 5/2^+ - 3/2^+ splitting. This procedure predicts three to five times larger values in the model FSS and fss2. The spin-orbit contribution from the effective meson-exchange potentials in fss2 is argued to be unfavorable to the small ls splitting, through the analysis of the Scheerbaum factors for the single-particle spin-orbit potentials calculated in the G-matrix formalism.
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