As James Sitar points out, the genre of Lycidas is complex. Genre encompasses the classifications of pastoral elegy and epic structures. The discussion of Milton's Lycidas having to do with "moving from pastoral poetry to epic poetry," asserts, essentially, that Milton incorporated features into Lycidas which were not standard to the genre of pastoral elegy and which suggested the English epic, bearing in mind that the epic form is of ancient origin beginning with Homer.
The particular characteristics that Milton intruded on the pastoral elegiac form are the introduction of the voices of Apollo as Phoebus, the River Cam as Camus, Saint Peter as the Pilot of the Galilean lake, and the uncouth Swain as the speaker of the lament to Lycidas. Each speaks and each has a persona, which are two characteristics of the epic put to grand use by Milton in this later epic Paradise Lost.
On the second point, pertaining to Milton's aesthetic of poetics (purpose of poetry) during Milton's time there was a great debate on the form poetry should have to be considered religiously proper. There were the Cavalier adherents, supported by the King and by the Laudians in the Church organization, and there were the Roundhead adherents, supported by the Puritan faction in the Church. The Cavaliers advocated a continuation of the tradition of poetry as exemplified by Spenser's and Shakespeare's diction and style, and the Roundheads advocated a direct simple diction and style that communicated a point without the embellishment of elaborate literary devices. Milton thought in accord with the Cavaliers.
In addition, it is apparent from his writing that Milton embraced the idea that poetry was to serve a social function in the tradition of Spenser and Shakespeare and the idea, well-developed in the Renaissance by Philip Sidney, that poets are the spokespersons of divine Providence and as such are given Inspiration to comprehend the ideals of divine conception and to convey these ideals to humanity, which seeks to know but lacks the needed Inspiration. For instance, poets might communicate the ideal Inspiration of the true qualities of love. In Lycidas, Milton upbraids the Clergy for failing the clergical ideal and accuses them of being imitation "Shepherds" of the "flock" of God and cautions that they will cut down in one blow by the double-edge sword of "the Lord."
[For assitional information, see Lycidas, Dartmouth College and "Milton's Salvational Aesthetic," Sheridan D. Blau.]