A Lunar Laser Ranging (LLR) system is to form part of geodetic instrumentation to be located at a new fundamental space geodetic observatory for South Africa. For optimal efficiency, LLR requires optical resolution or so-called astronomical seeing conditions of ~1 arc-second in order to deliver usable ranging data. Site characterisation should include a description of astronomical seeing for various locations on-site and overall atmospheric conditions. Atmospheric turbulence degrades astronomical seeing. In-situ methods of determining astronomical seeing are difficult, time-consuming and costly. We propose the use of a turbulence-resolving model to determine and predict astronomical seeing at a site. Large Eddy Simulation NERSC (Nansen Environmental and Remote Sensing Centre) Improved Code (LESNIC) is a turbulence-resolving simulation code which models atmospheric turbulence. It has been used to compile a database of turbulence-resolving simulations, referred to as DATABASE64. This database consists of a collection of LESNIC runs for a stably stratified planetary boundary layer (SBL) over a homogeneous aerodynamically rough surface. Results from DATABASE64 for the nocturnal boundary layer are employed to render profiles of the vertical distribution of optical turbulence (CN2 profiles). Seeing parameter values are also obtained by making use of DATABASE64 results. The CN2 profiles and seeing parameter values obtained from DATABASE64 results are compared with general observational results that have been published in the literature. The values obtained are consistent with results from field campaigns as reported. Turbulence-resolving models, such as LESNIC, show potential for delivering and predicting profiles and parameters to characterise astronomical seeing, which are essential prerequisites for establishing an LLR system at the most suitable site and most suitable on-site location. A two-pronged approach is envisaged – in addition to modelling, quantitative seeing measurements obtained with an on-site seeing monitor will be used to verify and calibrate results produced by the LESNIC model.