Easily fixable: Yes
Covered under warranty?: Maybe. It depends on the warranty
Here is a thread about the same thing from yesterday
When I bought my 4R in July, I also got a warranty that does cover this. (Toyota Gold) I didn't want to wait the 30+ days before I could make a claim, and the bulbs were on $6 each. I was annoyed enough that I just fixed it myself.
I also have a 2008 LTD, like you. The removal and installation process is the same, and it's really quick.
The unit is different between the Limited and non-Limited because of the dual-zone climate control.
If you can get dealer the parts counter person to let you look at the computer screen with him/her, you will be able to see exactly which bulbs you need. I brought my socket (to remove the one screw) and small flat screwdriver (for the bulb), and brought the thing right into the dealer to point out which bulbs were out. (The guy got confused and ordered the wrong bulb when I tried to order over the phone.)
If you let the service dept look at it, they want to replace the whole unit at a cost of something like $900 for just the part. Nice warranty scam, eh?
Update.
I did remove the faceplate as described and found the defective bulb. Swapped it to another position just to be sure it wasn't a socket problem. Sure enough it was the little bulb (about the size of Obama's brain) and got a new one at the Toyota Dealer, about $5 with MA tax.
This is actually my favorite part of this 4R. A lot of very serviceable parts, much better than other vehicles I've owned.
Bob