I contacted Lyman and they sent me a picture of what their carbide sizing dies look like. The one I have looks different from what Lyman pictured and what bersaguy pictured in Post #2 above, so I definitely believe what I have is a steel die. So Lube City, here I come!
Hold on there a second, JDinFbh. I'm really not trying to be a wise guy here, but knowing whether or not it's a carbide sizing die is a little more important than deciding whether or not to use lube.
And, the die in the picture bersaguy posted looks
exactly like my Lyman 38 Special/357 Mag
carbide sizing die.
The only part of a carbide sizing die that's actually carbide is the little, about an eight of an inch tall ring in the mouth of the die. It's important to know whether that ring is there or not because of how you adjust the die when you install it in your press. If it's just a regular steel die, you install your shell holder on the ram, and raise the ram all the way up. Then you screw the die into your press until it is touching your shell holder. Next, you lower the ram, and screw the die down about another 1/8 or 1/4 of a turn - so that your press "cams over" when you raise the ram again.
Okay, the steps for adjusting a carbide die are exactly the same except for the
last step. After you screw your carbide die in until it comes up against your shell holder, you BACK THE DIE OUT just a little bit - I like about the thickness of a piece of paper between my shell holder and the mouth of my carbide die. If you adjust a carbide die into your press until the press cams over when you raise the ram (like you do with a regular steel pistol sizer die) you'll bust that carbide ring right out of your expensive carbide die - lube or no lube.