If you wish to make a legal claim against someone, you may need to explain your legal claim in documents for the court (depending on the legal system). "Filing" documents can mean giving them to the court. A "lawsuit" means legal proceedings, usually civil or administrative proceedings rather than criminal, though I guess it could mean criminal proceedings depending on the context (compare the noun "suit", which can mean lawsuit [or various other things], with the verb "sue", which usually means to pursue civil proceedings against someone). In the expression "file a lawsuit", the words are being used slightly loosely. Logically, it refers to giving those documents to the court as the initial step in litigation. The real meaning is therefore basically that you are commencing litigation, and the expression could be used without the speaker imagining any particular documents.