Traditional song Lady Lune sang badly (4,4,4)

I believe the answer is:

auld lang syne

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'traditional song' is the definition.
The definition suggests a singular noun which matches the answer.

'lady lune sang badly' is the wordplay.
'badly' is an anagram indicator.
'lady'+'lune'+'sang'='ladylunesang'
'ladylunesang' anagrammed gives 'AULD LANG SYNE'.

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(Other definitions for auld lang syne that I've seen before include "New Year song" , "New Year's Eve favourite" , "New Year's Eve ditty" , "Hogmanay song" , "Old times, especially remembered with affection" .)

I've seen this clue in the Sydney Morning Herald.

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