I don't understand your first sentence.
Yes. Any law implies punishment if you don't follow the law, else it is useless.
If you ran a stop sign, and were convicted with a $100 fine, and next week the statute were changed to levy a $200 fine, would you have objection to the state billing you for a extra $100?
In the case of the Lautenberg amendment, a better analogy would be that next week the state changed the law to now saying that you could not own an automobile or vote because of the previous conviction.
And we are to believe that is not punishment, but merely "labeling"?