Thomas Tallis famously set the Lamentations in two versions, while the versions of Robert White and William Byrd are less well known.
Unfortunately (lamentably?), there does not seem to be a CD with the Tallis, Byrd, AND White versions for comparison. Magnificat recorded Byrd and White on Where late the sweet birds sang, while the Oxford Camerata recorded Talls and White on their disc of Lamentations! Dating on these compositions places them in Elizabeth's reign--yet they are written in Latin. Humanist that she was, the queen allowed Latin to be used in the liturgy at Court, at Oxford, and at Cambridge, since it would be understood in those venues.
Here is a recording from Magnificat of part one Thomas Tallis's setting of the Lamentations:
And here is a recording of the strepitus at the end of Tenebrae: