Lúkhag has led you to Dûn Traikh, presumably where she last saw Aighrig.
Lúkhag appears to know where she's going, but will need you to defend her.
Aighrig is determined to find Latharn.
Aighrig seems intent on confronting the Angmarim at the tower's entrance.
She has asked you not to attack them unless it's in self-defence.
The conversation between Latharn and Aighrig has not ended peacefully.