Lord Randall
Young Lord Randall, like many a young lad, isn't exactly the most forthcoming son. His mother has to coax his story out of him one question at a time (to which his answers are anything but clear). But this is way more than your average case of teenage silence. Here, it seems that our protagonist is suffering from a severe case of avoidance.
You know when something bad happens, and you don't want to talk about it because that would make it seem more real? We feel like that's sort of what's happening to poor Randall here. Instead of busting in and saying, "Mom, call 911! My girlfriend poisoned me, and my little dogs, too!" he draws out this tale of woe, and only admits the truth in the very end: he's been sorely betrayed by the one he loves, and to say it out loud seems to make it even more painful, for both him and us.
This method of storytelling reveals a lot about the teller. Lord Randall, it seems, is more of a lover than a fighter; instead of demanding vengeance right away, he draws out the story, so that the focus is ultimately his profound sadness (and weariness, to boot), not his anger. While some other versions of the ballad end in a more bloodthirsty fashion, with Lord Randall wishing hell and brimstone and various other punishments upon his murderous girlfriend, the classic version of the ballad that we're working with simply ends on this melancholy note of heartbreak. He lingers not on the act of poisoning—bless his heart—but instead chooses to focus on the emotional betrayal here.
A more pragmatic and literal-minded hero might have said something more straightforward (and less catchy) at the end, like "make my bed soon / for I'm sick in the gut, and am probably going to croak any minute," but that's just not Lord Randall's style. His insistence upon his weariness throughout the poem shows that he has come to terms with the major fact that he's about to die, but the thing he just can't get over the "sickness" of his lover's betrayal.
Lord Randall's Mom
Okay, you got us. We don't have much to say here. It's not like Lord Randall's Mother is a fully fleshed out character. And you can tell from her name (or lack thereof) that she's not exactly a real person. She's more like a tool of information; she's there to express concern and ask a ton of questions, so we can know what Lord Randall's been up to. We don't know anything about her, except that she's his mom, and frankly, we don't really need to. This poem may be a dialogue, but it's all Lord Randall's show, as far as we're concerned.
Lord Randall's Terrible "True Love"
We never actually meet this lady, but we know that she's a real… piece of work. Lord Randall's mysterious, poisoning girlfriend is the mysterious villainess of this poem, though we don't discover this until the last lines. She's the cause of his ambiguous sadness throughout (indicated by his emphasis on his exhaustion in his oft-repeated refrain), and all we know about her is that he loves her, but she clearly doesn't love him (or if she does, she has a right strange way of showing it). The fact that we don't have any motive for her motive of her supposed true love makes her all the more villainous. Boo! Hiss!