I came across several works, mostly fanfics, that depicted Lisanna and Lucy as rivals when it comes to Natsu. Most of them are Nalu fanfics, but that doesn't really mean anything. I strongly dissagree with the idea in general.
You see, I absolutely hate it when I see Lisanna depicted as a villain who wants to steal Natsu from Lucy, or the other way around. Lisanna's a sweet girl, and she may have been very close to Natsu, it doesn't mean she actually likes him that much. Maybe a lil' crush but it can also be questionned.
I kinda see Lucy and Lisanna as super pals who talk and laugh together at the stupid things that Natsu did.
Anyway, it wasn't really long, but I think you all got my point here.