TL;DR - On-topic
I think we can look to some of sister sites to help formulate our "policy" here as the same issue has been brought up before.
First, on English Language and Usage song lyrics are not out-right off-topic but come under some scrutiny. On their meta we find the following
If the question is about the grammaticality of line of poetry or what the metaphor is supposed to be, then that's OK. If it is about the cultural relevance of the item than that's off-topic. Source
I agree with that sentiment. While here on Literature we may not deal with grammar we certainly deal with metaphors and meanings. In addition, "General Reference" is no longer a close reason, so this would allow what might be considered "trivia questions" to be on topic as well. However, this should not prevent poorly researched questions from being down-voted.
Next, on Music Fans song lyrics are on-topic from what I can gather. They are also a newer site (older than Literature, but still in Beta) and still growing and learning as Literature is. On their meta we see the following discussion on lyrics:
First I think we have to realize that the meaning of lyrics may have multiple interpretations especially to different people. We should seek answers that are either:
- Interpretations from the person who wrote the lyrics.
- Commonly accepted interpretations.
The first should be preferred over the second, but lyricists sometimes don't explain their lyrics at all. In either case though a source should be required to keep the answers from just being personal interpretations which there could be infinite. Source
I also agree with this answer as we should try to find if the original author has commented on the issue, but if not other forms of literary analysis are obviously fine. Since Stack Exchange is a site for "experts" we should tailor our answers in that format.
Overall, I feel that the site will self regulate and that good questions and good answers will always rise to the top. Experienced users know how to identify the difference between a good and bad question and should respond accordingly, whether that be down-votes or closure.
Even if lyrics are on-topic they need to be formatted in a way that will not make them "Too Broad" or "Primarily Opinion Based".
(Full disclosure, I am a member but not highly active on ELU, and not a member on Music)