Musical settings have been composed by a number of composers, from the 16th C., Palestrina a. o. and Hebrew composers from the same time period, to several modern English composers a. o., and Bob Marley and Boney O.

There is no Hebrew version with that title; the early copies attrib. For David by Jeremias; a song of longing, and eventual revenge on the Daughter of Jerusalem. Versions for several uses.

There is a traditional round (...we lay down and wept...). Lee Hays and Don McLean used this as a basis for their version.

Versions use floods, rivers, and waters. Early English versions use flodes, floods.

Whose music do you use, or do you take it from a pre-1900 printing?
Whose lyrics do you use, or do you use those from pre-1900?

The various versiobns are interesting.

I would surmise that there are several valid copyrights on recent versions.