  Low-lying $\Lambda$ baryons with spin 1/2 are analyzed in two-flavor
unquenched lattice QCD. We construct $2 \times 2$ cross correlators from flavor
SU(3) ``octet'' and ``singlet'' baryon operators, and diagonalize them so that
we can extract two low-lying states for each parity. The two-flavor CP-PACS
gauge configurations are employed, which are generated in the
renormalization-group improved gauge action and the ${\mathcal O}(a)$-improved
quark action. Simulation are performed at three different $\beta$'s, $\beta =
1.80$, 1.95 and 2.10, whose corresponding lattice spacings are $a = 0.2150$,
0.1555 and 0.1076 fm. For each cutoff, we adopt four different hopping
parameters, ($\kappa_{\rm val}, \kappa_{\rm sea}$). The corresponding pion
masses range about from 500 MeV to 1.1 GeV. Results indicate that there are two
negative-parity $\Lambda$ states nearly degenerate at around 1.6 GeV, while no
state as low as $\Lambda (1405)$ is observed. By decomposing the flavor
components of each state, we find that the lowest (1st-excited) negative-parity
state is dominated by flavor-singlet (flavor-octet) component.
