  This Letter proposes a new search for confining dark sectors at the Large
Hadron Collider. As a result of the strong dynamics in the hidden sector, dark
matter could manifest in proton-proton collisions at the Large Hadron Collider
in form of hadronic jets containing stable invisible bound states. These
semi-visible jets have been studied theoretically and experimentally in the
fully hadronic signature where the unstable composite dark matter can only
decay promptly back to Standard Model quarks. We present a simplified model
based on two messenger fields separated by a large mass gap allowing dark bound
states to decay into pairs of oppositely charged leptons. The resulting
experimental signature is characterized by non-isolated lepton pairs inside
semi-visible jets. We propose a search strategy independent from the underlying
model assumptions targeting this new signature, and discuss the orthogonality
with respect to the existing searches. Remaining agnostic on the shape of the
di-lepton spectrum, we determine the sensitivity of a dedicated analysis to the
target signal. The proposed search can claim the 3{\sigma} evidence (exclusion)
of the heavier mediator up to masses of 3.5 TeV (4.5 TeV) with the full Run 2
data of the LHC. Exploiting the resonant feature of the lepton pairs can
enhance the sensitivity reach on a specific model. We estimate that an analysis
using the di-lepton invariant mass information can reach 5{\sigma} discovery up
to masses of 3.5 TeV and improve the exclusion up to more than 5 TeV.
