I hate to say so, but that wouldn't happen with the proper amount of proper lube.
Now, just a minute. Read on.
A lot of years ago, case lubing was often discussed in shooting related magzines. I distinctly remember them saying not to use such lubricants as common oils and greases. I can't swear to it, but I think lanolin was recommended at that time. Or of course, a lube made by one of the companies making reloading equipment.
Of the many types I have tried, I rate STP oil additive as the most heavy duty of them all, by far. As a trial I lubed one 30-06 case in the normal manner and sized it. I then sized another, which had not been lubed, then two more that had not been lubed! In other words, one normally lubed case had left enough lube on the die to allow the sizing of three more, dry, cases.
I don't see how it would be possible for a case lubed with STP to stick in a die. In normal lubing of every case, they come out like they had never been sized.
Most of the time I use one of the other types, like sizing wax or lanolin, because of the small amount needed and the much easier chore of cleaning the cases after.
You will likely get some good instructions on getting the stuck case out of the die.