You can find the tiles for the in-battle text box in unLZ. In a clean FireRed ROM, the number is 413:
http://i46.tinypic.com/s48j9v.png
However, what makes it tricky to edit is the offset it's at. I'm assuming you've found it in unLZ before, but you tried repointing it, and it broke your ROM when you did so. This is because the text box is located at the offset 0xD00000. This means that it's pointer in hex would be 00 00 D0 08. When unLZ repoints something, it actually doesn't know where the specific pointer for the image is, it just searches the entire ROM for a string that matches the pointers, then changes to whatever offset. Usually this isn't a problem, but for something that is originally located at 0xD00000, it is definitely a problem, because there are plenty of occurrences of the string "00 00 D0 08" in the ROM that aren't pointers to anything, so what happens is that unLZ changes them thinking that they are pointers when they're not (there's only 1 actual pointer to the in-battle text box, but unLZ thinks there's like 12 or something).
The solution is to manually find the offset to the actual string of 00 00 D0 08 that actually is a pointer to the battle text-box. I found all this out when I once did a quick experiment of altering FireRed's battle text-box to look like the one used in Emerald. Here's what I did:
1. Make a copy of a clean FireRed ROM that you don't mind destroying
2. Open it in unLZ
3. Go to 413, edit it enough so that it requires for you to repoint it, then click "Write to ROM"
4. If you repointed it into free space, a message should come up for every "pointer" that it changes (as I explained earlier, only one of these is an actual pointer). The messages will each say, "Pointer changed at __________" or something like that.
5. Open up Notepad (or physically get a piece of paper or a post-it-note, and a pen) and write down the offset of every "pointer" that unLZ changes
6. Your ROM should now be broken. No one cares about it anymore, so just delete it
7. Make another copy of a clean FireRed ROM
8. Open it with unLZ, insert a new battle text-box tileset into free space (when you click "Write to ROM", make sure you un-check everything)
9. Let's say you inserted new text box graphics at 0x71A240. That means your pointer, in hex, will be 40 A2 71 08
10. Now remember Step 5? We wrote down the offsets every "pointer" that unLZ told us. What this means that you wrote down every offset that the string "00 00 D0 08" occurs.
11. Looking at the offsets you wrote down in Notepad (or a piece of paper or whatever), go through each offset you wrote down with a hex editor, and manually change the string/pointer to where you inserted the new graphics (so as I said earlier, if you inserted it at 0x71A240, then your pointer would be 40 A2 71 08, meaning that you would go to the offset that you wrote down, and change the bytes there to 40 A2 71 08)
12. After changing one offset, did it break your ROM? Then change it back and try another offset. Keep doing it until you successfully repointed the battle texbox to the new one. Make sure you keep track of the specific offset of the pointer
13. Now that we have the actual pointer, open up your hack (Pokemon Sienna?), and using unLZ, insert new textbox graphics into free space
14. Open your hack in a hex editor, and go to the offset of the actual pointer that we found out during Step 12
15. Change the bytes there so that it points to wherever you inserted the new graphics
16. Ta-da!
Okay, I typed a lot more then I thought I was going to...