Low-lying　electronic　states　of　the　lutetium　dimer　(Lu-2)　were　studied　based　on　density　functional　theory　(DFT)　using　ten　different　density　functionals　together　with　three　different　relativistic　effective　core　pseudopotentials　(RECPs).　Relative　state　energies,　equilibrium　bond　lengths,　vibrational　frequencies,　and　ground-state　dissociation　energies　were　evaluated.　It　was　found　that　the　ground　state　is　a　triplet　state　irrespective　of　the　type　of　functional　and　RECP　used.　This　result　is　in　contrast　with　a　previous　DFT　calculation　which　gave　a　singlet　ground　state　for　Lu-2.　By　comparing　with　the　high-level　ab　initio　and　available　experimental　results,　it　is　evident　that　the　hybrid-GGA　functionals　combined　with　the　Stuttgart　small-core　RECP　yield　the　best　overall　agreement　for　the　properties　under　study.　The　effects　of　Hartree-Fock　exchange　in　B3LYP　functional　on　the　calculated　bond　length　and　dissociation　energy　of　the　ground　state　were　examined,　and　rationalized　in　terms　of　5d　participation　in　Lu-Lu　covalent　bonding.