I think it applies to only domestic travel. I know it sucks, but the government won't give any benefits without some tricks up their sleeve. As for LTA there are so many conditions and its just annoying.
As per rules only domestic travel is allowed.
That also has other conditions too.
And in a way it makes sense that since you are travelling here then you can get exemption here.
Could be many reasons: domestic travel needed; you need to be on “leave” from your company; you can only avail this once in 3 years. Check with your CA once, reason could be anything.