On the military and police style pistol lanyards a small split-ring like a key ring is used as the engineered failure point to break away if the item becomes entangled.

These rings are 1/4 to 1/8th inch in diameter and tend to have a small loop of 550 cord (about 4-5 inches long) tied between the item and split ring, then the split ring is attached to the lanyard.

I used to carry a Surefire Flashlight with wrist lanyard with no break away feature. I looped the lanyard around my thumb over the back of my hand and up the palm parallel to the flashlight body. The head of the flashlight stuck out the little finger side of my hand. If the flashlight ever got tangled I could open my grip and pull my hand free without the lanyard hanging up on my hand.

Hope this helps.
-joe