  It is quite basic in integrable systems to deriving Lax equations from
bilinear equations. For multi--component KP theory, corresponding Lax
structures are mainly constructed by matrix pseudo-differential operators for
fixed discrete variables, or by matrix difference operators for even-component
cases. Here we use Shiota method to construct Lax structure of 3-component KP
hierarchy and its reduction by introducing two shift operators $\Lambda_1$ and
$\Lambda_2$, where relations among different discrete variables can be easily
found. We believe the results here are quite typical for general
multi-component KP theory, which may be helpful for general cases.
