“No,” said Aslan. “I am sad and lonely. Lay your hands on my mane so that I can feel you are there and let us walk like that.” Would the girl's have done this w/o permission?

From the text:

And so the girls did what they would never have dared to do without his permission, but what they had longed to do ever since they first saw him buried their cold hands in the beautiful sea of fur and stroked it and, so doing, walked with him.