  On a class of four-dimensional Lifshitz spacetimes with critical exponent
$z=2$, including a hyperbolic and a spherical Lifshitz topological black hole,
we consider a real Klein-Gordon field. Using a mode-decomposition, we split the
equation of motion into a radial and into an angular component. As first step,
we discuss under which conditions on the underlying parameters, we can impose
to the radial equation boundary conditions of Robin type and whether bound
state solutions do occur. Subsequently, we show that, whenever bound states are
absent, one can associate to each admissible boundary condition a ground and a
KMS state whose associated two-point correlation function is of local Hadamard
form.
