Fighter of Lapis is a title given to the playable characters of the Fighters of Lapis games. It used in the stories as a term for any of the heroes participating in the story.
There seems to be no real requirement for being a Fighter of Lapis seeing as Wind-Up is one. It is suggested that the characters are chosen by the cosmos or perhaps by some greater being that exceeds even that of Morgan Freeman.
The term was first used in End of Days to refer to Mario's side. Since then it has been used to refer to the heroes in the story once the group gets a bit long to type out.