We study a supersymmetric version of the type-III seesaw mechanism considering two variants of the model: a minimal version for explaining neutrino data with only two copies of 24 superfields and a model with three generations of 24-plets. The latter predicts, in general, rates for μ-> e gamma inconsistent with experimental data. However, this bound can be evaded if certain special conditions within the neutrino sector are fulfilled. In the case of two 24-plets, lepton flavor violation constraints can be satisfied much more easily. After specifying the corresponding regions in the minimal supergravity parameter space, we show that under favorable conditions one can test the corresponding flavor structures in the leptonic sector at the LHC. For this we perform Monte Carlo studies for the signals, also taking into account the supersymmetry background. We find that it is only of minor importance for the scenarios studied here.