According to Oxford Learner's Dictonaries, the -'s suffix can have these two meanings:
(added to nouns)
1 belonging to
the woman's hat
Peter's desk
children's clothes
2 used to refer to somebody's home or, in British English, a particular shop
Shall we go to David's (= David's house) tonight?
(British English) I'll call in at the chemist's on my way home
So except for the last example, it looks like it's always used for people but not for things.
Is it really like that?
Song lyrics or Song's lyrics?