Aslan is there at the tombs, allowing Shasta to sleep in comfort against his back. Then he appears as a domestic cat, meek and mild. And before Shasta actually sees Aslan, knowing that he is something alive is enough to persuade him to tell of his sorrows. He is there at times of needs without being called.
Aslan looked after Shasta as a child, delivering him safely from the sea. He drove away the jackels from the tomb. And he saved Narnia by making sure that the horses travelled fast enough to get Shasta to King Lune in time.
The Aslan of 'The Horse and His Boy' judge and prosecutor. He punishes Avaris for her actions, and makes her understand the true nature of them. He mets out justice against Rabadash. But he is not unfair in his judgement- his wounding Avaris serves a double purpose; he gives Rabadash every chance to repent and effectively allows him to go unharmed so long as he lives in peace with his neighbouring countries.
Ultimately, Aslan is simply himself. He cannot be defined by known concepts, his nature defies true explanation. It is clear that in this name of Aslan, C.S. Lewis echoes the description of the Old Testament god as 'I Am'.