  We prove and apply two theorems: First, a quantitative, scale-free unique
continuation estimate for functions in a spectral subspace of a Schr\"odinger
operator on a bounded or unbounded domain, second, a perturbation and lifting
estimate for edges of the essential spectrum of a self-adjoint operator under a
semi-definite perturbation. These two results are combined to obtain lower and
upper Lipschitz bounds on the function parametrizing locally a chosen edge of
the essential spectrum of a Schr\"odinger operator in dependence of a coupling
constant. Analogous estimates for eigenvalues, possibly in gaps of the
essential spectrum, are exhibited as well.
