  We reexamine the spin-orbit splitting of 9 Lambda Be excited states in terms
of the SU_6 quark-model baryon-baryon interaction. The previous folding
procedure to generate the Lambda alpha spin-orbit potential from the
quark-model Lambda N LS interaction kernel predicted three to five times larger
values for Delta E_{ell s}=E_x(3/2^+)-E_x(5/2^+) in the model FSS and fss2.
This time, we calculate Lambda alpha LS Born kernel, starting from the LS
components of the nuclear-matter G-matrix for the Lambda hyperon. This
framework makes it possible to take full account of an important P-wave Lambda
N - Sigma N coupling through the antisymmetric LS^{(-)} force involved in the
Fermi-Breit interaction. We find that the experimental value, Delta
E^{exp}_{ell s}=43 pm 5 keV, is reproduced by the quark-model G-matrix LS
interaction with a Fermi-momentum around k_F=1.0 fm^{-1}, when the model FSS is
used in the energy-independent renormalized RGM formalism.
