i got a epi LP custom MIK.
i measured the neck before when i had nothing to do.
so a gibson 50s neck thickness.
1st fret - 20.8mm
12th fret - 24.5mm
my epi.
1st fret - 21.1mm
12th fret - 23.9mm
so you can say its basically similar to a 50s neck.
i have a gibson LP standard with 50s neck also, while the thickness is similar.
the gibson neck is slightly more rounder, so fits your hand nicer.
take note that an actual gibson LP custom neck is much thicker.
1st fret - 22.9mm
12th fret - 25.4mm