This conditional construction employs a ‘past perfect’ (had had) in the condition clause (protasis) as an irrealis to express the counterfactuality of that past eventuality, and a ‘past’ (would be) in the consequence clause (apodosis) to express the same counterfactuality in the present eventuality. This would be appropriate in this sort of situation:
He would be a rich man today if the song hadn’t had such an inadequate lyric.
That is, if the song had had a better lyric back then it would have sold much better over the years down to the present.
But in your example I don’t think it's the past inadequacy that makes the song less than great today: that’s caused by the fact that it still has those lyrics. Consequently I think what you want is an irrealis past in both clauses:
It would be a great song if it didn’t have such an inadequate lyric.
Incidentally, in actual grammatical studies we don't use the terms 'first, second, third conditional'—these are just teaching tools which don't represent any linguistic reality. You've clearly outgrown them, and you can discard them freely.