Question about Lune character (Burn)

[King]

When I apply burn to an enemy, does the burn dmg increase when I have perkz like 20% fire dmg on skill? (Lune weapon)

If burn is not affected by fire SKILL dmg, then its better for me to level my lighting weapon because the raw dmg on lighhtning is higher, thus 20% will be more beneficial there. I can grab the fire stain even for more dmg.

In short I'm hestitating whether to level my lightning or fire weapon on Lune...