I actually don't think Titus is really trying to interpret Lavinia's meanings at all, or at least is not really successful. Although long, passionate monologues are common in plays, I saw his (Titus') speeches as signs of madness. Even his brother Marcus tells him he's going a little far in what he's saying:
"Fie, brother, fie! teach her not thus to lay
Such violent hands upon her tender life" (3.2.21-2).
Though his intentions may be good and we're obviously supposed to sympathize with Titus for all the bad things that have happened to him and his family, I think at this point he seems insane, and is not really rationally trying to understand Lavinia, so much as just saying lots of random things as a result of his passion.
Conversation Piece - Monday, December 8, 2008
"Oh, come not near me, sir; I shall defile you.
I am that of your blood was taken from you
For your better health. Look no more upon't
But cast it to the ground regardlessly;
Let the common sewer take it from distinction.
Beneath the stars, upon yon meteor
Ever hung my fate, 'mongst things corruptible;
I ne'er could pluck it from him. My loathing
Was prophet to the rest, bu ne'er believed;
Mine honor fell with him, and now my life."
(The Changeling V.iii.158-67)
I am that of your blood was taken from you
For your better health. Look no more upon't
But cast it to the ground regardlessly;
Let the common sewer take it from distinction.
Beneath the stars, upon yon meteor
Ever hung my fate, 'mongst things corruptible;
I ne'er could pluck it from him. My loathing
Was prophet to the rest, bu ne'er believed;
Mine honor fell with him, and now my life."
(The Changeling V.iii.158-67)