Q: How close to the strings should the pickups on my Gibson Les Paul be?
A: Gibson recommends 3/32″ on the bass string side and 1/16″ on the treble string side. Measure the pickup height by fretting the low E string at the highest fret, and measuring from the bottom of the string to the pickup, then repeat for the high E string, fretting it at the highest fret and measuring its distance from the tp of the pickup.
You won’t hurt anything by adjusting the pickup height. Changing the pickup height can affect the tone, volume, intonation, and other factors in the performance of the guitar — use Gibson’s recommendation as a starting point, then experiment to find the height that you prefer.