what is the speaker's purpose in writing his "external line, " and what conditions are necessary for his purpose to be carried out?
I am going to answer your question two ways, and if I am off base please forgive me and feel free to ask a follow up.
1. If you are asking about "external rhyme", the process used by a writer to create a specific rhythm in his or her work by making the words at the end of the line rhyme then the purpose is to do just that, create a rhythm to be enjoyed and to be produced by the reader.
In order for this to work best these types of verse are intended to be spoken aloud and not read.
2. If you are asking about the line, "When in eternal lines to time thou grow'st", then he is using a "grafting" technique to graft the life of his object to eternity by his "eternal lines".
In order for this to be accomplished time has to continue and people have to read his lines. Otherwise the metaphor loses its import.