This Letter presents the results of a search for a heavy particle decaying into an e(+/-)mu(+/-), e(+/-)tau(+/-), or mu(+/-)tau(+/-) final state in pp collisions at root s = 7 TeV. The data were recorded with the ATLAS detector at the LHC during 2011 and correspond to an integrated luminosity of 4.6 fb(-1). No significant excess above the Standard Model expectation is observed, and exclusions at 95% confidence level are placed on the cross section times branching ratio for the production of an R-parity-violating supersymmetric tau sneutrino. For a sneutrino mass of 500 (2000) GeV, the observed limits on the production cross section times branching ratio are 3.2 (1.4) fb, 42 (17) fb, and 40 (18) fb for the e mu, e tau, and mu tau modes, respectively. These results considerably extend constraints from Tevatron experiments.