Ram was till the last moment willing to forgive Ravan, but Ravan could never bow down due to his own selfish reasons...first he was blinded, and secondly some authors analyse that Ravan could not back out as he lost every relationship in the war, so he could not come to a consensus after losing all his dear relations and preferred to die in the hands of Ram. Another concept is "vinash kale biprut buddhi"...Ravan got enough chances, where people tried to convince him that he was wrong, but he could not never accept that he was wrong.
Oh, I didn't know about the Laxam's part.
while My grandmother was reading the 7 books of ramayan, she was explaining us all the stuff ..
good to know this