I think it's a really sweet nn, but not as a given name.
Emmy sounds like a twee, babyish nn for Emma/Emily/Emmeline/Emilia or even Clementine or Clemency
Lou is a nn for Louise/Louisa/Lucy/Lucille/Lucinda/Luna/Lucia
There are so many nice, classic names there, you can choose two lovely ones and still have an Emmylou.
I think I'd go with Emily Lucia or Emily Louisa