ExplicitLorentzIndex[ind] is an explicit Lorentz index, i.e., ind is an integer.
Pair[LorentzIndex[1], LorentzIndex[\[Mu]]]\bar{g}^{1\mu }
Pair[LorentzIndex[1], LorentzIndex[\[Mu]]] // StandardForm
(*Pair[ExplicitLorentzIndex[1], LorentzIndex[\[Mu]]]*)