The Indian Lass was quite widely published on broadsides of the mid 19th. century.  There are several examples at  Bodleian Library Broadside Ballads  amongst which are:

The Indian lass  Printed between 1840 and 1851 by Samuel Russell, 24, Old Meeting Street, Birmingham
The Indian lass  Printed between 1858 and 1885 W. Fortey (late A. Ryle), Printer, Monmouth Court, Bloomsbury, London
The Indian lass  Printed c.1860 H. De Marsan, Dealer in Songs, Toy-books &c. No. 54 Chatham St. N.Y.
The Indian lass  Printed between 1863 and 1885 by H. Such, 177, Union Street, Boro', S.E. London
Indian lass         Printer and date unknown.

There are only fairly minor differences between the texts, and even the one printed in New York has "near Orleans" rather than "New Orleans".  Frank Kidson published a version from tradition in North Yorkshire (Traditional Tunes, 1891) with two tune versions (and the "tossing and tumbling" verse omitted, though the omission is indicated), and the Hammond brothers found versions in Dorset in 1906; one text (which does have "New Orleans") and tune (from two different singers) appear in Marrowbones (ed. Frank Purslow, EFDS 1965).  Purslow remarks:  "This fore-castle ditty would help pass away time on a dreary voyage.  Like most British songs it has crossed the Atlantic, where it is sometimes known as "The Little Mohee"."  Both of these traditional texts are very close indeed to the broadside versions.

Others consider the American song to be the original; see the entry at the  Traditional Ballad Index:
The Little Mohee  [Laws H8]

The text Joe has posted is a transcription from Jones' recording; pretty accurate, though "tongue" should be "tone" and "wail", "bewail".  There weren't any sleeve notes with The Noah's Ark Trap, but it looks to me as if Jones collated the Hammond and Kidson texts, and used Kidson's second tune (modified a little), which was noted down for Kidson by a Mr. Lolley (no original source named).  I'll send a midi of the notation from Kidson to Alan for the Mudcat Midi Pages.

Malcolm