  Low-lying $\Lambda$ baryons with spin 1/2 are analyzed in two-flavor lattice
QCD. In order to extract two low-lying states for each parity, we construct $2
\times 2$ cross correlators from flavor SU(3) ``octet'' and ``singlet'' baryon
operators, and diagonalize them. Two-flavor CP-PACS gauge configurations are
employed, which are generated with 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 from about 500 MeV to
1.1 GeV. The results are extrapolated to the physical quark-mass point. Our
results indicate that there are two negative-parity $\Lambda$ states nearly
degenerate at around 1.6 GeV, whereas no state as low as $\Lambda (1405)$ is
observed. By extracting the flavor components of each state, we find that the
lowest (1st-excited) negative-parity state is dominated by flavor-singlet
(flavor-octet) component.
