Renovation of the building stock in Europe is urgent to decrease the environmental impact from the building sector and meet the United Nations climate action goals. However, it is often hard to define a robust scenario for a renovation due to numerous uncertainties, which occur during the production, operation and end-of-life stage. One can cite the loss of performance of insulation and heating systems, the replacement time of installation or the future energy prices as well as the future climate. The replacement of oil boilers with heat pumps has shown a good performance regarding costs and greenhouse gas emissions. However, due to the flow and return temperature differences, often the current heat distribution system needs to be replaced as well, which is normally done with conventional radiators or floor heating. In this paper, we analyse a new possibility of a heat distribution system with earth plastered wall. We develop a methodology on the integrated assessment of life cycle assessment (LCA) and life cycle cost analysis (LCCA) for the renovation scenarios and adapt the analysis of the heat pump renovation solution with conventional radiators system and the earth plastered wall for two typical residential buildings located in Switzerland. Through rigorous statistical treatment, we then propagate the possible sources of uncertainty and perform the uncertainty quantification using polynomial chaos expansion to compare the distributions of two outcomes. The results show that the solution with the earth plaster has lower overall environmental impacts and costs. It has also been noticed that the solution with the earth plaster is more robust in investment cost and embodied emissions compared to the solution with the conventional radiators.