Well, yeah, you can do that (remove the lightning effects) and it will look normally like that.
You can also trigger it, so that the target unit is paused, when being under the effect of this bleeding (in case you play DotA, Fiend's Grip of Atropos does that). So, you will add your target and your hero in a unit group and make some saves via hashtable. If your Picked unit has a boolean saved on him, marked as "target", then remove life or make the caster damage him, else, if the unit is having a boolean saved, marked as "caster", then add life via Unit - Set life (To value) action.
I'd generally go for the triggered version, I prefer coding the spells I'm using :]