A couple of things to check.. Okay, more than a couple.. Lol
The first thing that I'd try is to check the timing of the extractor and holder grooves by taking your barreled action out of the Chassis/stock.. Loosen the grub screws enough that you can twist the barrel slightly while still fully in the receiver.. Now, close the bolt on an empty chamber. While gently twisting the barrel, you should be able to feel it stop in each direction of twist. Center the barrel between the stops and put a timing mark on the barrel and action so that you can see if the barrel moves out of alignment while torquing it down. Now, snug up the grub screws until they each just make contact with the barrel tenon. Then tighten each a little more while alternating between them until they are fully torqued. Now check to see if your timing mark shifted from center while tightening. It's possible that the grub screw cuts aren't aligned properly. This test can help you see if that might be the case.
Try pointing your Lilja barrel straight down at the floor and drop a live round into the chamber. Does it fully seat the rim against the breach face, or does the cartridge stop and leave the rim sticking up a little from being fully seated? If it's sticking up, how much pressure from your finger does it take to push it in until it's fully seated? CZ's are notorius for not being able to extract a live round that is engraving on the lands. But, the extractor groove can be modified to fix the issue. See below on how to do that.
How deep, or close to the chamber wall are the extractor slots cut? Compare the Lilja to your CZ barrel. If the wall thickness of the Lilja is significantly thicker, then that is probably your issue. A small needle file can be used to thin the metal in the groove which will allow the extractor claw to fully grab your case. Go slowly and carefully so that you dont file all the way through and into the chamber.
Check for burrs on the breach face at the edges of the extractor and holder grooves. If present, they need to be removed or else they can cause the bolt face to not fully close. This condition could cause an issue with your extractor and holder to not be able to fully engage the rim of the cartridge.
Are there any chips out of the extractor claw? I had one chip off at a 45° angle and it wouldn't extract a fired round. Happened in the middle of last year's NRL22 Nationals match.. My rifle wouldn't extract a live or fired round/case.
Have you taken the bolt apart? The C-spring that holds the extractor, holder and striker in place are very easy to stretch. If stretched, get a supply of new ones and replace. IMO, this is the weak link in the 457. The exposed striker and striker channel need to be cleaned periodically and the spring WILL eventually get stretched and need to be replaced.
Before performing any of the fixes that I mentioned, I'd recommend calling Carson at Lilja and let him know if you found something wrong with the barrel. Carson is a decent guy. Just calmly explain your problem and he'll get you taken care of.
Good luck, and let us know what you figure out.