I thought the "I am Myself" part is like the Burning Bush speaking to Moshe saying "I am who I am". The Tetragrammaton represents "I am who I am". And of course, the fact that it is said three times is a big clue.
The other scene I was thinking of was at the end of The Voyage of the Dawn Treader, where Aslan tells Edmund and Lucy they can never come back to Narnia, and Lucy asks if Eustace can't come back either, and Aslan asks if they really need to know that. That seemed to be a parallel to the final chapter of the Gospel of John, where the disciples come up out of the sea and eat fish with Jesus (like Lucy and Edmund did with Aslan), and Peter asks if John will never die, and Jesus replies "If I want him to remain alive until I return, what is that to you?"
EDIT.
Also, in The Silver Chair when Caspian dies and Aslan is crying over him seems like a parallel to Jesus weeping at the tomb of Lazerus. And the fact that it is only blood that can bring him back to life...
The glory of God is man fully alive--St. Iraneus
Salvation is a fire in the midnight of the soul-Switchfoot