the answer... I could not find... no matter how hard I tried
Feelings, sensations that you thought were dead...
So what was Ein to Ledah? How many missions had they been on together before their mission to Riviera? Whatever the nature of their relationship was, it was strong. Here is my explanation
A grim Angel purposely aiding the enemy and interfering with what supposedly is the will of the gods (magi by proxy) would be Fallen Angel, a traitor. Yet when Ledah meets Ein in Elendia, he hints at something Ein had no idea about - Yssgadril - then he vanishes. Almost as if trying to drop a hint to Ein.
He knows what Hector is up to, yet continues destroying the Aquariums keeping Yggdrasil alive and Ursula protected. He is even willing to fight Ein when Ein stands in the way of his tasks. Only after he is defeated and wounded by Malice does he tell Ein that Malice and Hector are not going by the gods orders, but Hector's own desires. He tells Ein they must be stopped.He explains the entire situation to Ein, who had thought all along that by destroying the Accursed, he had stopped the Retribution. It was as if he had no ability to stop himself from carrying out these false orders, so he relayed the truth to Ein so that Ein could stop them.
At this point he was injured terribly and may not have survived, which is why he used what strength he had to save Ein from Malice. His first act of complete freewill. As he lay dying, he admits that the distaste he had shown towards Ein was more than likely envy - envy of Ein's innocence, envy of his ability to decipher right from wrong, envy that Ein could question the orders given to him.
Whether a Grim Angel decides what they sacrifice or not is up for question. It could be that Ledah was told to give up his emotions by the Magi, or it could be that Ledah wanted to give up his emotions. Who knows how old he is, if he fought in the war against demons that occurred 1000 years ago. It could have been something he had to do or witnesses that made him want to purge himself of all emotions for the sake of simply being efficient and not having to deal with pain.
At any rate, Ein made him question himself. Ein had to have made him feel, something he thought he was incapable of doing. Sensations he thought were taken and forever lost to him. But he felt again, a desire that was his alone and not of the Magi. And the price he was willing to pay for such a precious gift was his life's blood.
Perhaps the answer he was seeking was his purpose as a Grim Angel. After learning of Hector's treachery, what is the purpose of a Grim Angel if they can so easily be lead astray by Magi who corrupt the words of the gods to bend to their own bidding. Hopefully he found the answer he was looking for and a higher purpose in helping Ein, his friend, the person who looked up to him and never once lost faith in him.