My personal intake of their relationship is that Natsu and Lisanna were potentially in love in their youth. Natsu managed to get over her death and move on and, after reuniting in their adult years, it has simmered down to a very close friendship, with them still caring for each other a great deal. I honestly can't see Natsu being serious enough to genuinely pursue a romantic relationship for all his loyalty, but I think that Lucy reminded him of Lisanna when they met, hence his protectiveness of her, most notably in the Phantom Lord arc when Lisanna's death was explored. I can't really see a romantic relationship between Lucy and Natsu, I feel like they're more than friends, but less than lovers, if that makes sense - but it's all very subjective and I can understand why people would, and I don't in any way indent to hate you just because of your preferences. In other words, I neither ship NaLu or NaLi, but I won't be too bothered if either become canon.