Well I hope so!!
I wonder in what contexts this could be used.
Could it mean that they are not family, that they do not have a professional relationship, or that they're not in a romantic/sexual relationship together?
Your second and third options are possible. The first options would best translate as:
"De rechter en de advocaat zijn niet gerelateerd" - "The judge and the lawyer are not related"
It can mean professional relationship or romantic/sexual relationship, in this sentence it'll almost always be the second meaning. Een relatie hebben isn't used like the English being related.
What is the difference between relation and relationship, English wise? Relation wasn't accepted while relationship was.
Relationship is between people, relation is more in the sense of relating concepts, that is how i understand at least, i'm not native btw
A relation can be relating concepts but when it refers to people, it means a family member. You can also use "relative"
if you said "The judge and the lawyer have no relation" I'd think you meant wither a) they are not family or b) there is no interaction between these careers