I see this as he is forcing himself to deal with his grief, and his process of dealing is the elegy. Milton is forcing himself to write and express his own grief. Milton spends the first stanza or so building the character of his departed friend to insure that the sense of his loss seems tragic. Milton brings up the question of Nature and why those forces did not save his Lycidas, but realizes that nature could not. Then he goes through a list of writers, mythical figures and what not and their grief at Lycidas' departure.
Life goes on.
Tomorrow to fresh woods, and pastures new. Shelley takes the elegy to a higher level. Shelley announces Keats' death, calls for mourning and then evaluates the tragedy of that death. In Lycidas, nature is question and that is all. Then nature moves on with the passing of winter and the onset of Spring once again.