Having read all of the RAVE manga, and seen the anime, and read the Fairy Tail manga, I'd have to say that yes, Lucy's relationship with Natsu is very similar to Haru's relationship with Lucy, and I say this even with Lisanna back in the fray.
Why? its because Lisanna hasn't made an effort to rekindle her old relationship with Natsu, and Natsu hasn't shown any interest in doing so himself. Meanwhile in the manga Natsu's relationship with Lucy gets lampshaded as romantic over and over again, with there being entire chapters with the two of them basically flirting around with one another. Just like one extra chapter with them and Lucy gets her fortune read and it says that she will spend her day with destined match, and Lucy just so happens to meet a nice guy (who is romantically interested in her), but when Natsu comes around she dumps the guy and goes on a mission with Natsu, spending the whole day with him.
Not only that but Elie in fact did have competition for Haru, the anime just didn't make it far enough both characters had competition for each other. Haru had serious competition in three characters (almost to the point where you questioned if he would really end up with Elie), and Elie had it in two, however they still got together at the end of the series.