The fact that a Lothsworn Drow attacks another Lolthsworn Drow on sight?
This is normal behaviour.
But is it?
What if the attacker is male and the female is a cleric of Lolth? Hell any female? Most males aren't Zaknafein and he even he kept up an outward veneer of respect..
Even away from that sort of set up, a Drow wouldn't attack on sight unless it was damn sure it would win. In many cases, even confidence of a win wouldn't be enough, they would also want to be sure of leaving no witnesses (that matter at least).
The Lolth loyal Drow absolutely are cruel and vicious but they are also scheming and very far from stupid or rash. This encounter could definitely do with some work from a lore/world building perspective..
