This event recalls the story in Daniel 3, where Shadrach, Meshach, and Abed-nego are thrown into a fire, and are seen, unharmed, with an angel in the conflagration. The similarities are superficial, for the point of the story in Daniel is that it was a real fire. In this story, it is a visible manifestation that appeared “as if by fire.” In Daniel, the three were thrown into the fire to be executed. In this story, the appearance of the fire prevents those who came to execute Nephi and Lehi from carrying out their purposes.
In both cases, of course, the deliverance was obviously perceived as a miracle, and led to freedom.