In the same way that dexterity adds to ranged attack bonuses, intelligence represents a more skill based bonus than power based bonus. Strength adds to melee attack and damage because it not just measures the ability to cleave through a defence with powerful blows, but also to deal more damage by dint of the same powerful blow.
If you want to add a stat for magical damage, and I can see the benefit at low level when base magical damage isn't fantastic, then consider adding charisma or wisdom bonuses to represent force of personality or will increasing the damage. Certain Vakeros spells add bonuses in this way, but then you are taking something away from a Vakeros...
The section about Magical Combat only says that the INT bonus is used for attack rolls. So "officially" there is no bonus for magical damage. (But of course a GM may choose to change it if he/she likes it better the other way.)
I think Confused Wolf is correct, but it's a surprising conclusion to me.
It means that magic is fairly weak in the LWRPG. Brothers of the Crystal Star really can't do all that much damage with lightning hand, even at higher levels. Lots of Valkeros magic specifically gives them bonuses to damage from their stat modifiers to address exactly this, I imagine.
This seems to contrast sharply with the books, where magic is extremely powerful. Banedon and Lone Wolf use magic to devastating effect on several occasions, often instantly killing their opponents.
Instead of that, Lighting Hand is a short range spell that's relatively weak. I wonder why, especially since it costs endurance.