Amiens' song in Act II, Scene VII applies to Duke Frederick's and Oliver's motivations in Act III, Scene I in that the song is all about "man's ingratitude" and friends "remembered not." Starting with Oliver, Oliver is Orlando's brother and, by the concepts of the 16th century, his friend also, meaning a person who is pledged to the good of another person in love and loyalty. Duke Frederick, as a ruler, is also positioned as a friend--in the same sense of doing good in a loving and loyal manner--to Oliver because Oliver is one of the Duke landholders and supporters, who exchange support and loyalty for beneficencies like land grants, positions at court and such.
Amiens' song perfectly describes Duke Frederick's and Oliver's motivations and mind sets in this scene because Oliver is trying to murder Orlando and has declared that, though his brother, he has never loved Orlando. Also, Frederick is threatening Oliver with the confiscation of his lands and wealth if he fails to deliver Oralndo "dead or living" to him.