The implementation of an X-ray mission with high imaging capabilities, similar to those achieved with Chandra (< 1 arc second Half Energy Width, HEW), but with a much larger throughput (2.5 m2 effective area @1 keV), represents a compelling request by the scientific community. To this end the Lynx/XRS mission is being studied in USA, with the participation of international partners. In order to figure out the challenging technological task of the mirror fabrication, different approaches are considered, based on monolithic and segmented shells. Starting from the experience done on the glass prototypal shell realized in the past years, the direct polishing of thin (2 mm thick) fused silica monolithic shells is being investigated as a possible solution. A temporary stiffening structure is designed to support the shell during the figuring and polishing operations and to manage the handling up to its integration in the telescope structure. After the grinding and the polishing phases, in order to achieve the required surface accuracy, a final ion beam figuring correction is foreseen. In this paper, we present the technological process and the results achieved so far on a prototypal shell under development.