There are criminal lawsuits and civil lawsuits.

As seen at:
http://www2.publicationsduquebec.gouv.qc.ca/dynamicSearch/te...

Code of Civil Procedure
...
2. The rules of procedure in this Code are intended to render effective the substantive law and to ensure that it is carried out; and failing a provision to the contrary, failure to observe the rules which are not of public order can only affect a proceeding if the defect has not been remedied when it was possible to do so.
http://en.wikipedia.org/wiki/Civil_procedure
These rules govern how a lawsuit or case may be commenced, what kind of service of process (if any) is required, the types of pleadings or statements of case, motions or applications, and orders allowed in civil cases, the timing and manner of depositions and discovery or disclosure, the conduct of trials, the process for judgment, various available remedies, and how the courts and clerks must function.

means the same as civil lawsuit but (i) the correct usage is always in the plural (ii) it is equally valid for EN-UK and EN-US, which lawsuit is not.