This is very definitely a fine example of pastoral poetry through the repeated reference to nature that Milton employs throughout the poem. However, it is also important to understand how Milton uses the genre of pastoral poetry for his own purposes, making it clear that the pastoral setting establishes an allegorical meaning that draws the reader's attention to the issues faced in his time and context. He does this through not solely relying on the motif of Greek and Roman mythology but also adding more domestic gods, who lie closer to home. For example, Camus, the god of the river Cam, that of course lies near Cambridge is referenced:
Next Camus, reverend Sire, went footing slow,
His Mantle hairy, and his Bonnet sedge,
Inwrought with figures dim, and on the edge
Like to that sanguine flower inscrib'd with woe.
Repeatedly therefore pastoral elements are established through the use of natural description to highlight the purpose of Milton in raising certain debates and issues central to his context, such as what value is a virtuous life when death can come at any time.
In the same way, religous elements are raised in this poem through the speaker's inclusion of religion as a comfort to the reader who has to live in such an uncertain world where death can occur at any moment. For example, not the following religious allusion towards the end of the poem:
So Lycidas sunk low, but mounted high,
Through the dear might of him that walk'd the waves...
The "him" is of course Jesus who famously walked on water as narrated in Matthew Chapter 14. Religion is therefore referenced through extensive Christian allusions that seek to offer the reader comfort and balm in response to the death of Lycidas but also the mortality that all humanity has to endure.