I can't help without specific model numbers. I think what you aren't getting is each LED light from each manufacturer has its own proprietary LED driver design that reacts differently to being dimmed. Lutron's technical documents are filled with specific lights from specific manufacturers and their associated compatibility. If you want the mystery solved, you just can't swap out incandescents for screw-in dimmable LEDs without understanding the compatibility issues.
My advice since you are not providing the model number for the LED bulbs - either call Lutron to get to the bottom of it or switch your bulbs back to incandescents, with advice toward the latter. The incandescents will truly dim much more than any LED bulb with the current technologies.
EDIT: If you were trying to provide an info link to the bulbs in post 276, the link is not there, FYI.