so i'm stumbled into a small question about that anti-heat eq quest

I got almost everything except the lava bucket. So where can i find that mithrill bucket to get the lava bucket required for crafting anti-heat eq

It's part of one of the other equipment quests you get from the weaver.

You need to go throu the anti-cold EQs to get a recipe, also you need to make a 3d mine