Is preparing for a lawsuit a valid reason to defer an exam?
Your original title seemed to imply you are talking about an ordered court appearance, which could be scheduled in conflict with an exam, in which case you should reschedule one or the other. If the court would refuse to reschedule, you would have fairly good reason to request the exam be delayed (I cannot answer the legal question of whether a school would be required to do so for that reason).

However, the body of your question makes it clear that you are just stressed out over a long time period. People are stressed out about all sorts of things. Other people in your program may have sick children or other family members, may deal with chronic illness themselves, may have to balance an additional job with their schoolwork, may have relationship problems, etc. Sometimes these issues are disruptive enough that a school may agree to give some lenience, and in some cases of disability or illness they may be required to, but for the most part you are expected to simply deal with them as part of life.

I can't know your specific situation, but being owed wages does not sound like it rises to the level of interruption that would require deferring an exam. You could consider asking, but this would probably be a favor rather than something you have a right to, so ask carefully if you must.