"Lycidas" is filled with allusions. As a pastoral elegy, the poem's very form alludes to a long history of classical poetry. From the Greek writer Hesiod on down, pastoral poets have written tales of shepherds, nymphs, and satyrs living in an idyllic countryside.
Milton's allusion to a wealth of classical gods and goddesses anchors this poem in the pastoral tradition. By calling on the "Sisters of the sacred well" (the Muses) for inspiration, lamenting that the "Nymphs" (female sea-spirits) couldn't save Lycidas from drowning, and fearing the wrath of the "blind Fury with th'abhorred shears" (Atropos—more usually called a Fate, not a Fury—the goddess in charge of severing the threads of human lives), the poem's speaker places this story of untimely death in a traditional Greco-Roman context.
He makes this clear, not just through his allusions to the old gods, but also through his allusions to old poetic traditions. When the speaker calls on the spirits of rivers to guide his pen—summoning the "fountain Arethuse" and the "smooth-sliding Mincius," for instance—he's also calling on poetic spirits of place, waters symbolically associated with the pastoral tradition. The Arethuse is a Sicilian spring; the Mincius, the river that runs through the great Roman poet Virgil's hometown. (And Virgil is important to this poem: his Eclogues inspire several major moments, like the shepherd's departure in this poem's final lines.) These allusions suggest that pastoral poetry flows from a particular time and place, that Milton is channeling an ancient, elemental kind of verse.
Rather than sticking strictly to the ancient world, however, the poem makes bold, surprising forays into other realms. For all that this poem follows a classical tradition, it's also tremendously British. Milton casts the coast off which Lycidas drowned in epic terms, speaking of mountains guarded by Druids (ancient Celtic priests and wise men) and the "wizard stream" of the Deva (that is, the river Dee, which marks the border between England and Wales).
He worries, too, about the threat to this enchanted coastline from "Namancos and Bayona[]"—that is, from Spain. That worry places the poem squarely in Milton's own time: a post-Reformation era in which Europe was torn between warring Protestant and Catholic factions.
Milton was a radical Protestant, a pious Puritan, and he felt that he was living through a war for the world's souls. His convictions become abundantly clear when he invites no lesser authority than the "pilot of the Galilean lake"—St. Peter himself, traditional guardian of the Christian church—into his poem. This deliberate anachronism makes it clear that Milton is turning the pastoral form to his own purposes. St. Peter's angry denunciation of corrupt Protestant clergy (not to mention his image of the Catholic church as a prowling wolf ready to snap up unguarded souls) transforms this into a contemporary political poem, not just an elegy.