the answer... I could not find... no matter how hard I tried

Little is known as to why Ledah became a Grim Angel, or what he was like before he became a Grim Angel. However, the Grim Angel Ledah we meet is rather cold and aloof. during the initial mission to Riviera with Ein, Ein's familiar, Rose, asks Ledah was was it that he had to give up to earn his Diviner- to which Ledah gives no reply...

In Heaven's Gate, Ein questions why the sprites must die, and with annoyance, Ledah tells him that they why is none of their concern- only fulfilling the will of the gods. When Ursula comes to bar their way, Hector demands that they kill her, and Ledah is more than willing to complay- until Ursula summons a wyrm. They pair defeat the wyrm, but Ursula vanishes with Ein. Ledah asks Hector how they will get Ein back, but Hector has already given up on Ein and considers him to be dead, whether he actually is or not.

We don't see Ledah again until he appears in Elendia after Ein has destroyed the second Accursed, questioning Ein's oath to Ursula to save Riviera. He wants Ein to return to his duties as a Grim Angel.

Ledah: So you're alive... Ein...
Ein: Ledah...
Ledah: Why are you siding with the enemy?
Ein: That's...
Ledah: We must activate the Retribution. Ursula is hindering us. It's not too late. Return to your post.
Ein: There has to be another way!
Ledah: We don't have time for that. Asgard is in danger... The best method is the destruction of Riviera.
Ein: But there's life here, too!
Ledah: You're letting your emotions interfere. If you won't pass judgment, then I will.
Ein: ...Ledah... What are you trying to do?
Ledah: ...Yggdrasil... (Ledah vanishes)

Ledah is finally confronted by Ein in Yssgadril as he is completing his mission to destroy the aquariums which keep the tree alive. His conversation with Ein is as follows:

Ledah:Hmph. You have fallen far. Without the Aquariums, Ursula will be unprotected.And Riviera will be finished...Knowing you, you will catch up, no matter what happens...So, I'll finish this now! Come, Ein...! (battle ensues)

However, Ein manages to defeat Ledah. Ledah then demands that Ein finish him off as That is the most practical action to take... in battle.... Instead Malice comes from no where and lands a critical blow to Ledah. Ein does not wish to leave Ledah's side, but Ledah insist that Ein stop Malice.

Ledah: How strange... You still think I'm your friend...? Besides... I'm not one to die here. You know that...Ledah... the Grim Angel... will not fall here...! Now what are you doing!? I said go!

After Ein defeats Malice, she tries a surprise attack, but Ledah flies in and takes the mortal blow meant for Ein. It is then he answers the question that Rose asked in the beginning of the game: what had he sacrificed for his Diviner? He confesses it was his emotions. Without emotions he could carry out his task without question.

Ledah: It seems... I made it in time...
Rose: (Ledah!)
Ein: Ledah! Why!?
Ledah: You are the most fit to carry out the mission. It's simple reasoning.
Ein: But you shielded me...!
Ledah: I understand now... Hector... is the source. Malice revived the Accursed... And Hector was the one that ordered it... So he could begin the Retribution. By returning Riviera to nothingness, Hector plans on becoming the one and only god. We were deceived by him. I have failed... as a Grim Angel... Heh...Familiar, long ago... you asked me...what I lost as a Grim Angel, correct? That which I lost... was my emotions... Thanks to that... I could manage any mission easily.
Ein: Ledah...
Ledah: You were nothing but a nuisance to me. Thinking, worrying, doubting... Watching you, I felt something similar to anger. But I realize now that wasn't anger... I may actually have been envious of you. You, who was as weak as a newborn child ...returned far stronger than thought possible. Ein... you might... You just might... be able to find it... The answer... I could not find... no matter how hard I tried as a Grim Angel... Farewell... Ein...
Ein: Ledah!
Rose: (Ledah!)
Ein: Ledaaaaah!
Ledah: ... (fades away in a shimmer)

It is later, as Ein goes after Hector and the Retribution does Rose note that the shimmering in Ledah's eyes as he faded away may have been tears.