If you're suggesting that the lag is because of the gradual application of the force (and overcoming of the blade's inertia), that doesn't explain the phenomenon
You're arguing in circles mate. It takes time to move? Of course it takes time. Start with zero displacement, and apply a force. The item accelerates while the force is present, and displacement increases at a greater rate. To reach its maximum displacement, use s+ut + 1/2 a t *2 and t = TIME.
Couldn't give 2 twopenny stuffs about a spacecraft in orbit, it has zero to do with a rotor in motion.