With the renewed interest for lunar surface exploration, the European Space Agency envisions to stimulate the creation of lunar communications and navigation services (LCNS) to enable, among others, autonomous navigation capabilities for lunar rovers. As the number of satellites foreseen in such a service is much smaller compared to Earth based global navigation satellite systems (GNSS), different complementary technologies are pursued to improve the attainable navigation accuracy for lunar rovers. One way to improve the position accuracy provided by the LCNS satellites is to constrain the vertical position using a high resolution digital elevation model (DEM). This article presents the results of a variance covariance analysis of an extended Kalman filter (EKF) implementation in which the LCNS ranging measurements are used together with DEM from the LRO LOLA instrument. Assuming a realistic orbit determination and time synchronization (ODTS) accuracy of the LCNS satellites, the usage of a navigation grade IMU and an oven controlled crystal oscillator (OCXO), a 3-sigma position accuracy of less than 10 meters can be obtained. Furthermore, the availability is substantially improved as the DEM aided solution enables a position solution in case of only 3 visible satellites.