Shepherds do their shepherding in the great outdoors, so it's no surprise that nature is everywhere in "Lycidas." We've got flowers, plants, bodies of water, even a few animals. The flora and fauna mourn for Lycidas, as if they could feel sadness the same way we do. The poem emphasizes that the young shepherd Lycidas was an important part of a pastoral, English countryside that seems downright dead without him.
The speaker blames nature several times for Lycidas' death, only to realize that nature isn't responsible for what happens to us. In other words, he learns that he can't personify nature or treat it like a human being.
Nature has to die (flowers are dead once they're picked) so that the speaker can deal with Lycidas' death, which shows us that nature is closely tied to the mourning process.