The lyricsplayground attribution is faulty. Lippa was born in 1927; 'nuff said. This song and "Big Rock Candy Mountain" are just some songs featured in Lippa's 2002 play.

The Naxos Ives compilation CD Troubador lists the available attributions for songs, apparently from the original releases. In every case, the attribution is "traditional", but in a few cases, Ives is additionally credited with arrangement. Consequently, I believe Ives thought of it as a traditional song, or at least was unaware of its provenance.

There is also this version, which may be a relatively modern merger of the Ives song with "The Soldier and the Maid", or may in fact be "traditional":

THE NIGHTINGALE

As I was out walking one morning in May,
I spied a young couple so fondly did play,
One was a fair maid and her beauty shone clear,
And the other was a soldier and a bold grenadier.

And they kissed so sweet and comforting as they clung to each other
They went arm in arm along the road like sister and brother
They went arm in arm along the road til they came to a stream
And they both sat down together love to hear the nightingale sing..

Then out of his knapsack he took a fine fiddle
And he played her such a merry tune as you ever did hear
And he played her such a merry tune that the valleys did ring
"Hark, hark," cried the fair maid, "Hear the nightingale sing!"

"Oh, soldier, oh soldier, will you marry me?"
Oh, no, pretty lady, however can that be.
For I've me own wife at home in me own country,
Two wives and the army's too many for me!

In the woods and the meadows beneath the bright moon,
Every lad with his lass makes the most of the June,
It's a shame that a handsome, young fellow like me,
Should be left, while the nightingale sings in the tree!"

"Oh, I'm off to India for seven long years
Drinking wine and strong whisky instead of small beer
And if ever I return it will be in the spring
And we'll both sit down together love to hear the nightingale sing."

Traditional; learnt from Ken Greenhough of the "Union Folk" c. 1968

The Virginia Company also performs another version:
The Nightingale: http://www.youtube.com/watch?v=Spqb7ZaCddk

The clip notes claim there are many versions, going back at least 400 years, but that may presume this particular song is indeed a variant of "The Soldier and the Maid"/"Hear the Nightingale Sing", which I don't think has been established. There is an old but unrelated song, "The Nightingale", which is often encountered in broadsides and collections; this, combined with the Ives title, may mislead those doing hasty research in regard to the song's actual age. But I find myself now leaning toward a "folk" provenance at least.