Specifically, this poem is considered a pastoral poem because of its idyllic setting. However, since that isn't one of your options, your better choice here is lyric. The second link I am providing gives the characteristics of both lyric and narrative poems, and as you will see, lyric is the better fit. Here's why:
Lyric poetry is highly emotional. Check--this poem is brimming with emotion, although it is debatable whether that emotion is beautiful love or just old-fashioned lust. It also has a musical quality, not meaning necessarily that it should be sung, but that it has a distinguishable rhythm. Marlowe's choice of rhyming couplets assures this quality. Lyric poems have a first-person narrator who idealizes the situation being described. The Shepherd, of course, speaks in the first-person and only tells his Love of all the wonderful benefits of coming to live with him; he leaves out all of the hardships that will come with the lifestyle of a shepherd.
Since a narrative poem should tell a story, and we don't get the other side of this tale until we read "The Nymph's Reply," you must classify this poem as lyric.