Damage Step, what the heck's that?
If you remember the rulebook, the Battle Phase is comprised of 4 steps:
Start Step (declare Battle Phase)
Battle Step (declare attack)
Damage Step (calculate damage)
So, basically, the Damage Step is when the actual damage is calculated, as well as when Flip effects are activated.
What's unique about the Damage Step is that, out of the three main steps, it's the ONLY step where Magic and Traps can't be activated. If you were to activate a trap like Magic Cylinder or Mirror Force, you would have to activate it during the Battle Phase, when the attack is first declared. If that happened, Lily's effect could not be activated, and her attack would remain at 400. So don't assume that you can wait for Lily to use her effect, then Cylinder her. It just won't happen.