I have Dillon carbide dies in 223 and 308. First, they are good dies and if I needed what they do, I would have no compunction using them. Second the entire die is NOT carbide, there is a carbide ring set into the steel around the bottom where the case first enters the die. The rest of the die body is steel so you need lube. I don't use them any more because they are tighter than my Redding and RCBS dies, they size cases more than necessary, and the carbide doesn't do anything that I cannot get with just lube. Mostly the oversizing is the issue.
If there is an expander (I never use them) I am pretty sure it is steel. I cannot swear to it but I am pretty sure I am right.
It would be amazingly expensive to make an entire FL die out of carbide and carbide is brittle so they would be really delicate. I have some carbide bullet dies and it cost a fortune to have them re-burned for a new profile.
By the way, if anyone cares the bullet dies are 6mm, designed for 68 grain flat based ogive 6 BR bullets, and I have three dies (squirt, core seat, and point up) that are for sale along with presses, a few hundred jackets and some lead, a bit of lube, squirt punches -- the whole nine yards. I just don't shoot BR any more. Speedy Gonzales burned the point up die because some damn fool chipped it - not me. I think the dies are from Simonson but I bought them a long time ago and I no longer remember.