So, original Painkiller game Black Edition seems to lag on new Windows OS, like Windows 10 or 11 a lot. Thus while googling the solution someone said that turning off Bloom in game settings could help. But it didn't. Heck, I saw people saying that turning off bloom does a little to nothing to reduce or completely remove the lag, and that's why I started experimenting with in-game graphical settings. And I guess that I found the solution to the problem. But, I'm not 100% guarantee that this will help you but you could try and see if it does anyway.
NOTE: This was tested on latest GOG version of the game!
So, the solution to the lag is not just by turning off bloom, but also turning off frigging Weather Effects and lowering down Particle Effects to Low. Mostly the weather effects, cause they are to blame, somehow, in this old game, for the lag. Thus, just start the game, then go to: Options/Video/Advanced/ and turn OFF weather effects, bloom AND reduce particle VFX to LOW, then apply the settings by clicking on the "Apply" in the lower right bottom of the screen. Done! Now your game should run smoother.
And yeah, it helped me personally because, back on Windows XP or Windows 7 this game didn't lag at all. It worked fine with all of that turned ON and on maximum graphics settings, but on Windows 10 however this game starts to lag for some reason. Go figure!
Also, as the last resort you can try out applying a compatibility with Windows 7 or even XP Service Pack 3 for this game and running it as the administrator. Just in case! But again, for me, turning off weather effects, bloom and reducing particle effects to low, did the trick.