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Brief Lives was a significant step in the series at the time, for one thing it was the first time readers saw the remaining sibling in The Endless family, Destruction. All the other six had made their first appearance at least two years prior. This arc was pivotal in defining Dream's family and took away a lot of the earlier mysteries about them. Some of his siblings had jumped in and out of his life throughout previous arcs and they had gathered for a brief meeting at the beginning of Season of Mists, but this saw more development for most of them then they had up until that point and better showed the interpersonal relationships between them.
More specifically, Brief Lives was the arc that established an identity for the youngest member of the family, Delirium, who would become the second most significant of Dream's brothers and sisters after Death.
In this arc, Dream was forced to become more involved with his family he had previously tried to shun and he found himself putting aside his own personal drama as an act of kindness towards his sister which ended in him doing things he had never intended, developing his character into that of a much more selfless being. The consequences of these actions would have a huge impact on his personal journey and the series as a whole.
Thus, Brief Lives became the turning point in the series, beginning the journey to the already inevitable end of Dream's death.