We consider models of supersymmetry that can incorporate sizeable mixing between different generations of sfermions. While the mixing is constrained by the nonobservation of various flavor-changing neutral current processes, there exist regions of the SUSY parameter space where the effects of such mixing can be probed at colliders. In this work, we explore this possibility by focusing on the slepton sector. The sleptons are produced through cascade decays in direct neutralino-chargino (χ20χ1±) pair production at the Large Hadron Collider (LHC). The final state is characterized by three leptons and missing energy. We probe the lepton-flavor-violating (LFV) vertex arising in χ20 decay by identifying a distinct and unambiguous combination of the trilepton final state containing a lepton pair with same flavor and same sign (SFSS) in addition to a pair with opposite flavor and opposite sign (OFOS). This combination of a trilepton final state containing both OFOS and SFSS pairs can not only suppress the SM background but also differentiate the flavor-violating decays of χ20 from its corresponding flavor-conserving decays. We present results showing the sensitivity of lepton-flavor-violating parameters for a wide range of slepton and chargino-neutralino masses. In addition, we also illustrate signal significance for various points in the parameter space, taking into account background contributions assuming two luminosity options (100 and 1000 fb-1) for the LHC run 2 experiment at s=14 TeV.