  We consider solutions satisfying the zero Neumann boundary condition and a
linearized mean field game equation in $\Omega \times (0,T)$ whose principal
coefficients depend on the time and spatial variables with general Hamiltonian,
where $\Omega$ is a bounded domain in $\Bbb R^d$ and $(0,T)$ is the time
interval. We first prove the Lipschitz stability in $\Omega \times
(\varepsilon, T-\varepsilon)$ with given $\varepsilon>0$ for the determination
of the solutions by Dirichlet data on arbitrarily chosen subboundary of
$\partial\Omega$. Next we prove the Lipschitz stability for an inverse problem
of determining spatially varying factors of source terms and a coefficient by
extra boundary data and spatial data at intermediate time.
