  We study conformal transformations of indecomposable Lorentzian symmetric
spaces of non-constant sectional curvature, the so-called Cahen-Wallach spaces.
When a Cahen-Wallach space is conformally curved, its conformal transformations
are homotheties. Using this we show that a conformal transformation of a
conformally curved Cahen-Wallach space is essential if and only if it has a
fixed point. Then we explore the possibility of properly discontinuous groups
of conformal transformations acting with a compact orbit space on a conformally
curved Cahen-Wallach space. We show that any such group cannot centralise an
essential homothety and that for Cahen-Wallach spaces of imaginary type must be
contained within the isometries.
