Summary: Previous papers dealt with the quantization of the Lemaître-Tolman-Bondi (LTB) model for vanishing cosmological constant \(\Lambda \). Here we extend the analysis to the case \(\Lambda > 0\). Our main goal is to present solutions of the Wheeler-DeWitt equation, to give their interpretation and to derive Hawking radiation from them. We restrict ourselves to a discussion of those points that are different from the \(\Lambda = 0\)-case. These are mainly to do with the occurrence of two horizons.