Since this poem's dialogue form is pretty darn obvious, you guys are about to roll your eyes in a minute. but bear with us. This poem, being a dialogue between mother and son, really sounds like a dialogue between mother and son. What we mean is, even though these characters are only barely sketched out, we can still hear their relationship in the way they speak to each other, formulaic and typical though it may be.
We can imagine Lord Randall's mother being any worried mom, whose questions grow more and more panicked as she realizes that her son has been murdered of all things (what happened to the normal kinds of mischief, like cutting class and shoplifting?). Lord Randall, like anyone who's just suffered a terrible heartbreak (and been poisoned, to boot), responds with a kind of depressing quietness, as though he can't bear to tell his loving mother the truth.
While the mother's lines seem more dramatic and fraught with emotion, Lord Randall's lines are equally emotional because they express the dreadful weariness and sadness of betrayal. A perfect example is the heart-wrenching finale to this ballad, in lines 17-20:
"O I fear ye are poisoned, Lord Randall my son!
O I fear ye are poisoned, my handsome young man!"
"O yes, I am poisoned: mother, make my bed soon,
For I'm sick at the heart, and I fain wald lie down."
We can just hear the hysterical panic of Lord Randall's mother, but then he answers with a calm resignation that's a whole lot more effective and a whole lot more of a bummer than it would be if he'd freaked out. Also, remember that this poem would have originally been performed to music: imagine two actors singing this song in highly dramatic, maybe even over-the-top, tragic fashion, à la Broadway musical… and now we're picturing a very special Renaissance episode of Glee. So there's that.