In recent years, the Moon has gained renewed interest in terms of human exploration for scientific purposes. In this context, Thales Alenia Space is leading a consortium to define the main concepts for a Lunar Radio Navigation System (LRNS) in terms of Orbit Determination and Time Synchronization (ODTS) as part of an ESA Technology Development Element (TDE) programme. This work focuses on the latest performance results achieved through a dedicated simulator in terms of Signal In Space Error (SISE).