A search for heavy right-handed Majorana or Dirac neutrinos NR and heavy right-handed gauge bosons WR is performed in events with energetic electrons or muons, with the same or opposite electric charge, and energetic jets. The search is carried out separately for topologies of clearly separated final-state products (“resolved” channel) and topologies with boosted final states with hadronic and/or leptonic products partially overlapping and reconstructed as a large-radius jet (“boosted” channel). The events are selected from pp collision data at the LHC with an integrated luminosity of 139 fb-1 collected by the ATLAS detector at s=13 TeV. No significant deviations from the Standard Model predictions are observed. The results are interpreted within the theoretical framework of a left-right symmetric model, and lower limits are set on masses in the heavy right-handed WR boson and NR plane. The excluded region extends to about m(WR)=6.4 TeV for both Majorana and Dirac NR neutrinos at m(NR)