Lang attribute and "old" latin

All,

As far as I know, current screen reading technology only supports a limited
number of languages.  

I am in the process of reviewing a number of web documents that feature, in
part, a fair bit of "old Latin" (circa 13th century - it's a cool academic
project).  At any rate, W3C guidance states "Clearly identify changes in the
natural language of a document's text and any text equivalents (e.g.,
captions)." *AND* the ISO code for Latin is either "LA" (ISO 639-1) or "LAT"
(ISO 639-2) so clearly this *CAN* be done.

As well, wikipedia suggests that "Screen readers without Unicode support
will read a character outside Latin-1 as a question mark, and even in the
latest version of JAWS, the most popular screen reader, Unicode characters
are very difficult to read."  (Is this true, I was not aware of this.  The
document often uses þ throughout this old Latin text - is this going
to be an issue?)

The question is, is there any real advantage gained by adding this
information (lang="lat") to the content?  It is/would be a huge undertaking,
and if *not* done is pedantically/dogmatically wrong (fails WCAG P1 4.1),
however I am at a loss to explain any real value in doing it to the client
as at the end of the day I cannot myself find a "real justification" that
would improve the accessibility of the document.

Thoughts, arguments (either side) and other support gratefully accepted.

Cheers!

JF