Several new physics models that extend the Standard Model require the existence of Long-Lived Particle (LLP) as a solution for the problems like Dark Matter and Naturalness. The new ATLAS Phase-II setup with its huge statistics and updated detectors offers an opportunity to probe the yet unexplored region of the phase space. For muon spectrometer based searches neutral LLP decaying to collimated jets of leptons and light hadrons (lepton-jets) are of great interest. These particles offer an unique signature that can lead to an early discovery. New triggering techniques and algorithm have been developed and studied to improve the selection of both highly and poorly boosted lepton-jets.