Núrelleth wants the memory of Faengris to live on in Lórien and to do more than simply slay some Orcs in his name.
Núrelleth is silent for a moment.
'Do not misunderstand me, ${PLAYER}. I am grateful for Cúbenn's thoughtful gift of this arrow, and I am pleased that the Orcs could be made to pay for the death of my husband...but it is not enough. I cannot put into words how important Faengris was to me, but vengeance upon the Orcs would in no way repay them for what they have taken from me.
'No, instead I want the memory of my husband to live on in Lothlórien. I want to tell my people what he was, and why it is such a sorrow that he is gone.
'There is a lonely tree on the bank of Anduin, just east of Imlad Lalaith. Bring this arrow to that tree and set it at its base. Faengris and I would watch the sun rise in the east sitting by that tree, and I would like this arrow to remain there in remembrance of him.'
The lonely tree where Núrelleth wants the vengeance arrow placed is on the bank of Anduin, east of Imlad Lalaith.
Núrelleth wants the Elves of Lothlórien to remember her husband Faengris, and to that end, she would rather the vengeance arrow stand in his memory rather than be used to slay more Orcs.
Núrelleth is on Telain Glorelloth, on one of the flets that extends over the hedge that encircles Caras Galadhon.
You have left the vengeance arrow at the lonely tree as Núrelleth requested of you and should now return to her.