This is blatantly an excuse. Lord Randall isn't just tired from hunting. He's tired from life (as we'll find out later).
Quote #2
"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.