Which verb means to drive or urge someone on?

The verb that means to drive or urge someone on is "goad." Goading involves encouraging or provoking someone to take action, often in a persistent or irritating manner. This term captures the idea of pushing someone to do something, whether it’s to provoke a reaction or to inspire them to complete a task. This form of urging can be both motivating and, at times, frustrating, depending on the context in which it is used.

The other choices do not relate to urging or motivating in the same way. For instance, "fawn" implies showing excessive affection or flattery, which does not inherently involve driving someone to action. "Lucid" refers to clarity of thought or expression and does not have the connotation of urging. Lastly, "eulogy" involves a speech or tribute praising someone who has died, lacking any relation to the idea of urging someone onward. Thus, "goad" stands out as the most fitting choice for the meaning of urging someone to take action.