If Gauche had arrived to get Lag late or hadn't mad it at all, Lag might have died of exposure, starvation or having his heart eaten by a Gaichuu. Small wonder Lag refuses to abandon Niche, who's in a similar situation as an undelivered piece of Human Mail.
Nelli is shown wielding a knife with some skill in her first appearance, and is able to inflict a wound on Lag's arm, so her claim that she'll kill Jiggy if he doesn't show any remorse over his death most likely isn't bluster. Consider that Jiggy isn't the most emotionally expressive individual, so it's likely that Nelli would have concluded that he wasn't sorry enough and tried to kill him if Lag hadn't helped her see the truth.
