  The aim of this paper is twofold: First, we characterize an essentially
optimal class of boundary operators $\Theta$ which give rise to self-adjoint
Laplacians $-\Delta_{\Theta, \Omega}$ in $L^2(\Omega; d^n x)$ with (nonlocal
and local) Robin-type boundary conditions on bounded Lipschitz domains
$\Omega\subset\bbR^n$, $n\in\bbN$, $n\geq 2$. Second, we extend Friedlander's
inequalities between Neumann and Dirichlet Laplacian eigenvalues to those
between nonlocal Robin and Dirichlet Laplacian eigenvalues associated with
bounded Lipschitz domains $\Omega$, following an approach introduced by Filonov
for this type of problems.
