You should check more dictionaries. I have heard of Longman's dictionary, but it certainly isn't the top choice. For British English, always check Oxford and Cambridge dictionaries. I believe Google uses Oxford as default. For American English, check Websters.
Oxford has the following as a primary definition for "innocent":
"a street quite innocent of bookshops"
So, your example means that the song was "lacking" any logical coherence.
As "innocent" can also means that someone is naive, in this context there is a further implied meaning that the songwriter is perhaps unaware that their words lack coherence, and so is something of a jibe at their lack of ability or experience.