We study self-interacting dark matter signatures at the Large Hadron Collider. A light dark photon, mediating dark matter self-interactions, can bind dark matter particles to form a bound state when they are produced via a heavy pseduoscalar in pp collisions. The bound state can further annihilate into a pair of boosted dark photons, which subsequently decay into charged leptons through a kinetic mixing portal, resulting in striking displaced lepton jet signals. After adapting the analysis used in the ATLAS experiment, we explore the reach of the model parameters at the 13 TeV run with an integrated luminosity of 300 fb^-1. For heavy dark matter, the displaced lepton jet searches can surpass traditional monojet signals in setting the lower bound on the pseduoscalar mass. If a positive signal is detected, we can probe the dark matter mass and the dark coupling constant after combining both the displaced lepton jet and monojet searches. We further show the CMS dimuon search can be sensitive to the final state radiation of the dark photon. Our results demonstrate terrestrial collider experiments complement astronomical observations of galaxies in the search of the self-interacting nature of dark matter.