Explain how a lion passed without attacking him and the arm of a commoner can hold fire and yet not be burned in "Julius Caesar".
That is exactly the point. These things typically wouldn't happen. Lions are predators...they attack when they're hungry. It's possible that the lion isn't hungry, but then again, why would it be in the streets of Rome at all? No man--regardless of his social status--can hold fire in his hands without risking severe burns.
Strange things are occurring, and the men are discussing the meaning of these omens. Shakespeare often uses paranormal and eccentric events as well as abnormal weather to indicate internal conflicts (should I or shouldn't I do this thing...) and/or displeasure from the universe/higher power toward the issues at hand. For instance, Cassius is attempting to talk Casca, Brutus, and others into killing Caesar.
The events on this night indicate to us, the reader, that no matter how poor an idea it is to have Caesar as King or Emperor, killing him is an even worse idea. By using these strange events, Shakespeare is giving the reader a hint (foreshadowing) that bad things will happen should these men go through with their plan to kill Caesar.