Well ... this has already been done with other microcontrollers, so it might be possible theorically, but concerning practice ...
Here are some informations I found looking on the internet for the same reasons (I actually have 2 TI-89, one has its screen broken):
http://www.ubasics.com/adam/electronics/ti/link/tilink.shtmlhttp://lpg.ticalc.org/prj_tilp/ : provides a Link Protocol Guide for all TIs, which you are going to realize soon it is not so simple ...
Good luck, keep posting on this forum if you can make anything

By the way, there should be easier ways to interface Arduino with an LCD screen !!!