Don't think all scientific name started with L. Might be a wrong spelling where you got your info from.
Just for reference, there are many families for the wrasses.
Mainly seen here are:
- Anampses
- Halichoeres
- Cirrhilabrus (Fairy wrasses)
- Coris (Yellow, Green, red wrasse)
- Pseudocheilinus (Six line, Mystery)
- Macropharyngodon (Leopard wrasse). The picture above which Lemon looking for belong this family.