"Where gat ye your dinner, Lord Randall my son? Where gat ye your dinner, my handsome young man?"
Lord Randall's somewhat nagging mom begins by asking another familiar parent-type question: "Where did you eat?" ("gat" being a Scottified version of "got"). Her son totally can't just head off to bed without having eaten.
Note how her questions follow the same formula, ending in "Lord Randall my son" and "my handsome young man." This is a classic trait of the British ballad form (for more on this, see "Form and Meter"). This kind of pattern is the same thing we see in a song like "The Twelve Days of Christmas," in which a formulaic set-up—for example, "On the nth day of Christmas, my true love gave to me…"—helps us remember and keep track of the evolving list of things.
It's the same deal here.
"I dined wi' my true love; mother, make my bed soon, For I'm weary wi' hunting, and fain wald lie down."
Lord Randall, who's not exactly the most forthcoming of speakers, answers that he dined with his true love. That is, he had a dinner date with his special lady friend. His main squeeze. The love of his life.
And again, the refrain comes back. Get used to it, since it'll appear in every stanza. Again, the emphasis on Lord Randall's exhaustion jumps out at us. We don't know what's wrong with him yet, but we're getting a bad feeling about it.
After all, he is asking his mother to make his bed for him, right after he's saying he dined with his true love. Shouldn't he be less exhausted and more in a good mood?