  We present our latest study of Lambda-Nucleon (LN) interaction by using
lattice QCD, following up on our report at LATTICE 2008. We have calculated not
only the scattering lengths but also the central and tensor potentials, which
are obtained from the Bethe-Salpeter (BS) amplitude measured in lattice QCD.
For these calculations, we employ two different types of gauge configurations:
(i) 2+1 flavor full QCD configurations generated by the PACS-CS collaboration
at $\beta=1.9$ ($a=0.0907(13)$ fm) on a $32^3\times 64$ lattice, whose spatial
volume is (2.90 fm)$^3$, with the quark masses corresponding to
$(m_\pi,m_K)\approx (301,592)$, $(414,637)$, $(570,724)$ and $(699,787)$ (in
units of MeV). (ii) Quenched QCD configurations at $\beta=5.7$ ($a=0.1416(9)$
fm) on a $32^3\times48$ lattice, whose spatial volume is (4.5 fm)$^3$, with the
quark masses corresponding to $(m_\pi,m_K)\approx (512,606)$, $(464, 586)$ and
$(407,565)$. The following qualitative features are found: The LN potential has
a relatively strong (weak) repulsive core in the $^1S_0$ ($^3S_1$) channel at
short distance, while the potential has slight attractive region at medium
distance. The tensor potential is found to be weaker than the $NN$ case. These
results hold in both full and quenched QCD. The energy of the ground state on
the finite lattice volume is calculated: In both spin channels, energy shift
due to the finite volume, from which we extract the scattering length via the
L\"{u}scher's formula, is found to be negative at all values of quark masses,
suggesting that the LN interaction is attractive. We have also discussed the
quark mass dependences of the potentials and the scattering lengths.
