Dave --

But "lie" does not not fit the rhyme scheme. Overall, scheme of the song is: A/B/A/B-C/D/C/D. "Lie" would make it A/B/A/B-C/D/D/D.

But yeah grammatically, "lay" is correct. It would be a bit wierd, but you could fix the grammar by switching the second half of that verse to the present tense:

"A gent comes riding by,
in a one-horse open sleigh.
He laughs as there I, sprawling, lie,
and quickly drives away!"

(finally, truth in advertising about all this "winter wonderland" stuff!)