Definition: involving mourning or expressing sorrow for that which is irrecoverably past
It’s a form of “elegy,” which is “a poem of serious reflection, usually a lament for the dead.”
Why I Looked It Up
In a book about the sports performance of Black athletes:
Almost every attempt to decipher the East African mystique includes an elegiac description of the warrior spirit of the Kalenjin.
Kind of an odd usage, since the entire section was about how the Kalenjin people of Kenya dominate distance running. The race of people isn’t dead, and, I assume, neither is their “warrior spirit.”
I think perhaps it just means “serious” or “with gravitas.”