  We consider the possibility that the muon g-2 anomaly, $\delta(g-2)$, finds
its origins in low energy supersymmetry (SUSY). In the general MSSM the
parameter space consistent with $\delta(g-2)$ and correct dark matter relic
density of the lightest neutralino easily evades the present direct LHC limits
on sparticle masses and also lies to a large extent beyond future LHC
sensitivity. The situation is quite different in GUT-defined scenarios where
input SUSY parameters are no longer independent. We analyze to what extent the
LHC can probe a broad class of GUT-inspired SUSY models with gaugino
non-universality that are currently in agreement with the bounds from
$\delta(g-2)$, as well as with the relic density and the Higgs mass
measurement. To this end we perform a detailed numerical simulation of several
searches for electroweakino and slepton production at the LHC and derive
projections for the LHC 14 TeV run. We show that, within GUT-scale SUSY there
is still plenty of room for the explanation of the muon anomaly, although the
current LHC data already imply strong limits on the parameter space consistent
with $\delta(g-2)$. On the other hand, we demonstrate that the parameter space
will be basically fully explored within the sensitivity of the 14 TeV run with
300 fb$^{-1}$. This opens up the interesting possibility that, if the g-2
anomaly is real then some positive signals must be detected at the LHC, or else
these models will be essentially ruled out. Finally, we identify the few
surviving spectra that will provide a challenge for detection at the LHC 14 TeV
run and we characterize their properties.
