Yeats wrote "The Lake Isle of Innisfree" in 1890 and "Sailing to Byzantium" in 1928. The dates are significant: the first poem represents a young man's desire to escape from the pressures of busy modern life while the second poem reflects the longing of an old man not to die.
As Keats does in "Ode on a Grecian Urn," Yeats asks why the human body (or that of any natural creature) must grow old, decay, and die, and like Keats, he turns to art as a contrast: why cannot we, like works of art, remain eternal and ageless?
As Yeats's speaker metaphorically sails for Byzantium in the first stanza, he launches his theme immediately. The land the speaker ventures toward is "no country for old men." Instead, it is a place where one can focus on neglected "monuments of unageing [sic] intellect," in other words, art.
How do we combat aging and fight becoming "a tattered coat upon a stick," which is Yeats's image of what an old man looks like? One way is through song or poetry.
How else can a "dying animal" (i.e., an aging person) be gathered into "eternity"? Yeats's speaker says that if he could, he would become a work of art. He says in particular he would like to become an object "of hammered gold and gold enamelling / To keep a drowsy Emperor awake." He would also like to be a mechanical bird "set upon a golden bough to sing." Aging and death are the problem. The poet turns to ageless art as the answer. To write about this, you need to find quotes from the poem that show or suggest the poet grieving about aging and death and then quotes that show his solution in art.