There are many depictions of lions or lion-men in ancient near eastern
art, but did lions actually ever live in this area? If not from where
did these near/middle eastern rulers go lion hunting?

Of course there were lions in the Near East.  Hercules wore a
lionskin, Samson jawboned one to death, the Lion of Judah, plus all
the depictions in art that you refer to, right down to the paintings
of the Orientalists in the 19th century.  But I don't know when the
last lion was actually seen in the Near East.  Searching for lions and
extermination and Near or Middle East get lots of political sites,
from Alexander to the Crusades, Armenians and Holocaust.

http://dspace.dial.pipex.com/agarman/bco/lion.htm
"The Asiatic Lion (P.l.persica), once to be found throughout India,
the Middle East and Southern Asia, is today, only to be found in the
Gir Forest National Park in Gujarat, western India, where the
population is estimated to be in the region of 290. The male of the
Asian species has a less prominent mane compared to that of the
African male and both sexes display a long fold of skin that runs the
length of the belly which is not found on the African species."

last Anatolian lion was killed in 1950 in Manisa-Turkey.