As I understand it, the Speer Lawman is supposed to be loaded to exactly the same ballistics, and thus have the same recoil and POI, as Gold Dots of the same weight. Speer listst the Lawman .380 at 950fps from a 3.75" barrel while Winchester lists their .380 FMJ at 955fps but no barrel length is given. I wonder if Winchester's velocity figure is from a longer barrel and thus the Speer is a bit faster from the same barrel length. If such is the case, it could simply be that your recoil spring needs to take a bit of set and that the Lawman was simply hot enough to overcome this while the Winchester wasn't.
Another possibility is that the OAL of the Winchester is a bit different due to the flat nose bullet. I've heard that Winchester began using flat nose FMJ bullets in their .32 Auto loadings in order to make the OAL short enough to fit in the magazine of a Seecamp (the Seecamp was originally designed for Winchester Silvertips and most FMJ loadings are too long to fit in the magazine), I wonder if the same treatment was given to their .380 loadings. I have noticed that my Walther PP .32 Auto doesn't like the flat nose Winchester 71gr FMJ but that it doesn't seem to have issues with any other brand of ammo. You might simply try another brand of ammo that uses round nose FMJ such as Federal, Remington, S&B, or Fiocchi to see if any of them give you the same issues.