How we cite our quotes:
"For I'm weary wi' hunting, and fain wald lie down." (4)
This is blatantly an excuse. Lord Randall isn't just tired from hunting. He's tired from life (as we'll find out later).
"For I'm sick at the heart, and I fain wald lie down." (20)
This final version of his refrain tells us that our guess about Lord Randall's feelings was right; his exhaustion is an expression of his melancholy, and here, he admits that he's brokenhearted.