This study investigated the relationship between dream lucidity, i.e., a dreamer’s insight to the ongoing dream, and attention by considering lucidity as a trait. We examined the ways in which lucidity correlates with the orienting, alerting, and conflict components of the attentional network. A total of 77 participants rated the lucidity of their dreams over 7 consecutive days with the LuCiD scale and then completed the attentional network task (ANT). A negative correlation between trait lucidity and the conflict score of the ANT was found for 49 participants whose responses were faster when an alerting signal was presented. This result suggested that, with a prerequisite that the presence of cues facilitates subsequent information processing, the greater a person’s trait lucidity, the more efficiently he or she is capable of resolving conflicts.