In the poem "Luke Havergal" by Edwin Arlington Robinson, the identity of the speaker (the one who narrates the poem, if you will) is never conclusively revealed or confirmed. Many have offered supposition in one direction or another: Satan or a demon speaking and acting for Satan, connected to the supposition that the theme of the poem is the speaker's work to convince Luke Havergal (of the title) that suicide is the only way out of his misery and suffering; or the woman whom Luke Havergal lost sometime before the instance the poem discusses, although any evidence for that interpretation of the speaker is nominal at best and fabricated at worst, since the poem refers to the woman in the third person ("if you listen she will call" [line 6]), which is something speakers rarely do of themselves; or even Luke Havergal himself, as though he were posing (hypothetically, and not outright in the poem) questions to himself and then giving himself answers in a monologue or only in his head; or someone else entirely.
Having likely eliminated the deceased woman, or even her spirit, as the speaker, since she is mentioned twice more in the poem (in the third and fourth stanzas respectively as well as the first) but always in the distant, emotionless third person point of view and nothing more intimate or personal than that, we may turn to other possibilities.
Luke Havergal himself seems next least likely to be the speaker if we continue to remember that people rarely refer to themselves or address themselves (even in their own heads in mental arguments) by their own names. (Consider: when was the last time you addressed yourself: "Well, Self, today is the day"?) Therefore, the references to Luke's name in the first and fourth stanzas, especially with such deliberate repetition (his full name is mentioned six times in the poem in total), seem to imply that he himself is not the speaker, either. Further, the use of the pronouns "you" in lines such as "But go, and if you listen she will call" (line 6) and "Out of a grave I come to tell you this" (line 17); and "your" in lines like "the fiery night that's in your eyes" (line 10) and "That flames upon your forehead with a glow" (line 19); and the use of the implied "you" in the many suggestions (or commands) throughout the poem in lines such as "Go to the western gate" (line 1) (which might as well read "You, go to the western gate, Luke Havergal") are indicative of someone other than Luke Havergal himself being the speaker/narrator of the work.
Finally, the continual reassurance and encouragement the speaker offers to Luke Havergal that suicide is the only way out of his misery seems to offer the most evidence for the interpretation of the speaker as a demon or even Satan himself, working to entice Luke to end his own life so he can see his beloved once more in death, even when suicide might well have been considered a mortal sin in Christian circles (hence the argument that "God slays Himself with every leaf that flies, / And hell is more than half of paradise" in lines 13-14). Death is even painted in gently appealing terms and phrases via the musicality of the lilting meter and rhythm of each line ("And in the twilight wait for what will come" in line 3, for example) and the abundance of repeated consonant and vowel sounds in alliteration and assonance respectively (e.g., the letter "w" is used thirteen times to excellent lyrical effect in the first stanza alone), painting an almost soothing, enticing picture of the idea of death for Luke to contemplate and even act upon from someone who seems to have a vested interest in being convincing.