Let's start by saying that Thoreau was a pretty well-informed dude. And that's putting it lightly. Many of the allegories that he uses in Walden are actually citations of parables from various non-Christian religious or philosophical traditions, including Hindu, Arabic, and Confucian sources. Not only is Thoreau knowledgeable enough to include these citations, but in doing so, he gives us a sense of how universal his personal quest is. He situates himself rather self-consciously in a global philosophical tradition meant to emphasize the universality of his unique experiment.
One of the most striking allegories in Walden is actually one that Thoreau essentially made up on his own. It is the tale of the artist of Kouroo that appears in his "Conclusion." In the story, this artist becomes so absorbed in making a staff that he remains impervious to Time (insusceptible to it, immune to it, not affected by it... you get the point – he doesn't notice Time passing). This is a fitting allegory for Thoreau's own project in writing Walden. The fact that the allegory is an invention of Thoreau's – there's no such story in the Bhagavad-Gita, the Hindu sacred text – makes things even more interesting. Thoreau seems to have internalized his readings of ancient philosophy to the point where he can write his own allegorical stories, but in the voice of these ancient storytellers. Cool.