While Fed law (FOPA 86) protects you during transport for modern firearms, and MAY be applicable (if your LEBEL is a "firearm" under the law), you need to ensure that it is an "antique firearm" under the laws of your destination state.
In your case, Illinois law needs to be complied with while you are in the state.
Generally, other than the age of the gun, there is also some kind of language about "ammunition not being available".
This is where you might run into difficulties, as you said you have blanks for the gun. It might be argued that because you have blanks, it is not an antique. (Blank ammunition is still ammunition under some laws).
Safest course is for you to spend the money needed, and have a lawyer get a ruling from the state (IL) about your particular gun, and how it is covered under the law. Get that in writing, on official letterhead, and CARRY IT WITH YOU when you are in Illinois! (assuming your gun is recognized as exempt from the "modern gun" laws).
If your gun is recognized by the state as being exempt from regular gun laws, you need something from the state, in writing, and have it with you at all times when you have that gun in their state.
Most law officers are not going to be familiar with the details of the law, and NONE OF THEM are simply going to take your word for it.
What they are going to see is , "its a gun, you've got it, and you don't have the FOID card, so you're under arrest..." Run into this even once, and the cost of having that gun already proven exempt under the law (official document from the state) will be well spent.
A friend of mine has a registered antique motorcycle. Under the law where he lives (and has the bike registered) he is not required to wear a helmet when he rides that bike. (like a old car before seatbelts).
When he rides without one, he carries a copy of the law with him. He still gets stopped, and when that happens, he shows the officer his copy of the law.
He tells me that gets him out of about HALF of the tickets. The other half of the time, he gets a ticket, with the officer saying, "IF you are right, the judge will throw it out." And they do. But he still got a ticket....
With a gun, in a state like IL (permits required), better to be on rock solid legal ground, before you run into a well intentioned but under-informed officer.
Of course, if the state of IL does not recognize your gun as an antique, then all the regular gun laws apply.
