I would spray out the inside of the die, there is probably a bunch of lube that got pushed around in there and wound up on the shoulder.
And as mentioned,
that seems like a buttload of lube. I have never used the Lee lube, and have converted to the home brew lanolin.
I also do not do anything special on the necks, I do the spray and then roll them around in a plastic shoebox, I am sure the necks seem to get enough.
If you mix something, this is also why you want the 99% alcohol, you do not want to leave any moisture behind. I also mix a very light lanolin ratio,
just put enough in that it looks like a beer that is probably not very good, like Bud or Coors Light.
How are you cleaning after sizing? I would have some concern on getting all that neck lube out of the case.
Also, since you are using Lee dies, if you do get a stuck case it is fairly easy to pound it out with the decap-expander rod. If you are using a progressive you can do this in a few steps (I run twice for rifle rounds, size one the 1100 and load on a 650).
Also since you are using Lee dies, know that
Squirrel Daddy has expanders for .223, and they are Strong Like Bull.