In the event that R-Parity conserving supersymmetry (SUSY) is discovered at the LHC, a key issue which will need to be addressed will be the consistency of that signal with astrophysical and non-accelerator constraints on SUSY Dark Matter. This issue is studied for the SPA benchmark model based on measurements of end-points and thresholds in the invariant mass spectra of various combinations of leptons and jets. These measurements are used to constrain the soft SUSY breaking parameters at the electroweak scale in a general MSSM model. Based on these constraints, we assess the accuracy with which the Dark Matter relic density can be measured.