Divine Wraith versus Lily

[Cardinal]

My question is:
IF I had Injection Fairy Lily on the field, and my opponent had Divine Wraith set, would they be able to use Divine Wraith's (effect) to destroy Lily.
When I attack using Lily's effect paying 2000 lp, or is it too late as it says on Lily, that its effect kicks in during the damage step?.

 

[Entropy]

Lilly can be hit by Divine Wrath. DW can be activated in the Damage Step, since it's a Counter Trap.

 

[HorusMaster]

It still wouldn't negate paying the cost in order to boost Lily. The player controlling Lily will still lose 2000 LP.