Niobium is a ductile transition metal of growing interest for several technological applications, thanks to its intriguing characteristics, among them high melting point, moderate density, good ductility, high corrosion resistance and superconductivity. By contrast, its use is limited by some weaknesses lied to the mechanical properties, which can undermine the quality of the surfaces worked by metal forming processes. Sheets of pure Niobium can be used for the manufacture of extremely customized components and a flexible process like the incremental sheet forming fits well with this manufacturing philosophy; in fact, this technique does not require complicated tools and/or dedicated equipment and is capable to respond quickly to the market demands. The scope of this paper is to investigate the influence of the tool/sheet contact conditions on different features like the forming loads, the surface quality and the occurrence of failures, when pure Niobium rolled sheets are formed incrementally. To this aim, the simplest variant of incremental sheet forming, namely single point incremental forming, was considered by using a common fixed end forming tool with hemispherical head. The process was carried out under dry and lubricated tool/sheet contact conditions, following the indications from a preliminary campaign of wear tests conducted by a pin-on-disk apparatus. The experimental campaign highlights the strong influence of the tool/sheet contact conditions and the importance of a correct choice of them on the features investigated, in order to limit the forming forces and the risk of failure, as well as to preserve the surface quality of the components made by incremental sheet forming of Niobium.