for all we know, lena might not be well-versed in the rules of engagement--which vampires can pass the gift, who can receive it. she's new to this, after all. another consideration: when she's about to bite cop-boy, she's conflicted about quite a few things, including whether to commit him to the horrors of her new life versus wanting to save him and be with him. maybe her desperation made her forget the rules of vampiric transmission. maybe in the moment she isn't thinking properly, and then her not biting him is the resolution of that internal conflict, or the putting-off till later of the decision to turn him.
in other words, i think that bite-deferral scene can be interpreted in a variety of ways, and that's cool. this sort of haziness makes for a richer viewing experience in my (reflectively reddish) eyes.
also, i'm ok with all the female vampires killing off all the known male vampires but behaving just as badly as they accuse male vampires of behaving. with serious power comes temptation and all that. and they're vampires--they're supposed to misbehave, unless they have major willpower.