Sustainable management of aquifers requires long-term predictions of their aquifer-scale groundwater balance under climate change with meaningfully quantified uncertainty. In our analysis, we account for uncertainty in model parameters, measured data, model errors, stochastic model inputs (e.g., rainfall, potential evapotranspiration), and climate scenarios. To afford this analysis, we rely on an extension of lumped hydrological models that includes groundwater flow and storage, called lumped geohydrological model (LGhM). It shows good model performance and is three orders of magnitude faster than 2D or 3D numerical groundwater models. We use Markov chain Monte Carlo (MCMC) for Bayesian inference on a calibration period to quantify posterior parameter uncertainty and lumped data-and-model error. Then, we perform Monte Carlo forward runs with stochastic weather inputs under three different climate scenarios to quantify uncertainty in long-term predictions up to the year 2040. We apply our approach on a virtual reality representation of the Wairau Plain aquifer, New Zealand. We hypothesize that the variability in future climate is the most important impact factor. To test this hypothesis, we disentangle the overall uncertainty between data/model, parameters, weather, and climate inputs. We expect our approach to be highly useful for arbitrary types of catchments because the LGhM model structure can easily be adapted.