Pretty easy to describe.
When a ball is drilled standard it is called a T grip.
Thumb pitches and finger pitches are oriented to a line that goes straight from the center of the thumb to dead in the center of the bridge.
The CLT leaves the thumb pitch oriented to the center of the bridge.
BUT the fingers are oriented to a line that is drawn between the middle and ring fingers. The idea is that for most righties this line points to the right of the thumb. For most lefties this line points to the left of the thumb.
Most shops don't even bother unless the difference in the regular Tgrip line and the natural finger line is at least 10 degrees.
The result of the CLT(or what I think of as Natural finger line). Is that if applies the same pitches they had in the Tgrip the middle finger ends up with forward pitch and the ring finger ends up with reverse. From this comes a slightly increased axis tilt and lower track. (slight).
Advocates of the CLT(not me) also claim the natural orientation of the fingers leads to more comfort and revs also.
Me, I get a little less in the revs department.
Mr. Buzzsaw UK uses a slightly different method where he does the above but pitches the thumb differently.
Also just so you know there is a thumb offset method that is different and reorients the finger pitches off the thumb and the thumb pitches pointed more at the middle finger. The theory here is that no human thumbs are in straight line with h the middle of their middle and ring finger but that most people's thumbs instead are more in line with their middle to index finger when in a bowling grip!
Chickens are the exception to this!
REgards,
Luckylefty