The term "lay down" is used improperly in the case of the ABBA song. But keep in mind that the term "
lay down and die" has also become a frequently used term and could even be considered an idiom nowadays to mean "give up."
Remember in songs, the songwriter also must often bend phrases and words in a way perhaps not always proper in grammar but more "conversational" to convey a certain feel or mood.
In the example you give, the word "lay" is also an "inside rhyme" with the previous line's "May". This helps to break up the frequent rhyming sounds of try,might, die and I, so "lay" would be the better choice regarding writing the song.
So its more about taking poetic license with songwriting and not so much about being grammatically correct.
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