FWIW:
My LCP did not come with the CT Laser, I purchased it shortly after I purchased the pistol..
After putting the Laser on I found it to be shooting high/left at 5 or so yards.
It was a simple adjustment, windage and elevation to get it perfect..
I actually wound up zeroing in my CT Laser at THREE yards as that's the personal self defense range I use with my mouseguns. (7 yards for my larger caliber pistols).
I'm thinking a zero at 3 yards is still pretty much zero at any other reasonable self defense distance.
FWIW, I'm very pleased with the LCP and the CT Laser.
Best Wishes,
Jesse