  We argue that in order to account for the muon anomalous magnetic moment
$g-2$, dark matter and LHC data, non-universal gaugino masses $M_i$ at the high
scale are required in the framework of the Minimal Supersymmetric Standard
Model (MSSM). We also need a right-handed smuon $\tilde\mu_R$ with a mass
around 100 GeV, evading LHC searches due to the proximity of a neutralino
$\tilde{\chi}^0_1$ several GeV lighter which allows successful dark matter. We
discuss such a scenario in the framework of an $SU(5)$ Grand Unified Theory
(GUT) combined with $A_4$ family symmetry, where the three $\overline{5}$
representations form a single triplet of $A_4$ with a unified soft mass $m_F$,
while the three $10$ representations are singlets of $A_4$ with independent
soft masses $m_{T1}, m_{T2}, m_{T3}$. Although $m_{T2}$ (and hence
$\tilde\mu_R$) may be light, the muon $g-2$ and relic density also requires
light $M_1\simeq 250$ GeV, which is incompatible with universal gaugino masses
due to LHC constraints on $M_2$ and $M_3$ arising from gaugino searches. After
showing that universal gaugino masses $M_{1/2}$ at the GUT scale are excluded
by gluino searches, we provide a series of benchmarks which show that while
$M_{1}= M_{2} \ll M_3$ is also excluded by chargino searches, $M_{1}< M_{2} \ll
M_3$ is currently allowed. Even this scenario is almost excluded by the tension
between the muon $g-2$, relic density, Dark Matter direct detection and LHC
data. The surviving parameter space is characterised by a higgsino mass $\mu
\approx -300$ GeV, as required by the muon $g-2$. The LHC will be able to fully
test this scenario with the upgraded luminosity via muon-dominated tri- and
di-lepton signatures resulting from higgsino dominated $\tilde{\chi}^\pm_1 \,
\tilde{\chi}^0_2$ and $\tilde{\chi}^+_1 \, \tilde{\chi}^-_1$ production.
