"Lycidas" is a poem that mourns the death of Milton's college buddy Edward King, whom he refers to in the poem as Lycidas. You're probably wondering why in the world Milton would write a poem for his best friend and opt to call him by an old Greek name, instead of just calling him, say, Eddie. But there's more at work here than mourning the death of a friend. Using the name "Lycidas" has its poetic advantages.
Who was Theocritus? Glad you asked. This guy was a Greek-speaking poet who lived in Sicily in the third century B.C.E. He is often credited with inventing the pastoral genre – that's right, inventing it. Virgil was a famous – perhaps the most famous – Roman poet, who wrote The Aeneid, one of the most famous epic poems ever written. Before he wrote that whopper, he wrote a series of pastoral poems called the Eclogues, which were (and are still) arguably even more famous than Theocritus' Idylls.
Lycidas is a pastoral elegy, which we talked about briefly in "In a Nutshell." These poems have a tradition in which the poet gives the dead person whom they're mourning a name from the works of Virgil, Theocritus, or other similar poets. For example, Percy Shelley calls his poet friend John Keats Adonais in his pastoral elegy of the same name.
Lycidas, as you might have guessed, isn't just a randomly chosen name. As it turns out, in Theocritus' Idylls, Lycidas is called the "best of pipers." (Lo and behold, Milton's Lycidas is one heck of a musical talent, too.) Even though he is praised by Theocritus' speaker, however, he loses a singing contest. Virgil's Lycidas is also quite the talent, although he expresses some doubts about his poetic abilities. Despite the fact that Virgil and Theocritus use the name Lycidas for different purposes, one thing is clear: Lycidas, while a talented singer, either loses out to another poet or fears that he will.
The Lycidas of Theocritus and Virgil bears some strong similarities to Milton's schoolmate King. By calling him Lycidas, Milton is drawing attention to the fact that King was himself a budding poet, and a good one at that. But Milton also draws attention to himself as a poet. By writing about a guy named Lycidas, Milton might be signaling to his readers that he sees himself as on par with the greats like Theocritus and Virgil, who wrote about the same dude (sort of). It's a bold move, but considering that Milton is one of the most famous and loved poets in the English language, you might say he knew exactly what he was doing.