The dark photon (A'), the gauge boson carrier of a hypothetical new force, has been proposed in a wide range of Beyond the Standard Model (BSM) theories, and could serve as our window to an entire dark sector. A massive A' could decay back to the SM with a significant branching fraction, through kinetic mixing with the SM photon. If this A' can be produced from decays of a dark scalar that mixes with the SM Higgs, collider searches involving leptonic final states provide promising discovery prospects with rich phenomenology. This work presents the results of a search in 2015 ATLAS data for A's in the mass range of 0.2 to 10 GeV decaying into collimated jets of light leptons and mesons, so-called "lepton-jets". No deviations from SM expectations are observed. Limits on benchmark models predicting Higgs decays to A's are derived as a function of the A' lifetime; limits are also established in the parameter space of A' mass vs kinetic mixing. Complementary to various other ATLAS A' searches, lepton-jet analyses will continue to expand in model coverage and in parameter space as data-taking continues at the LHC.