I am currently working on an idea for fiend pact warlock whose patron is a demon lord seeking redemption through the aid of said warlock, but I am having a difficult time figuring out *why* a demon lord would desire such a thing.

A demon lord probably wouldn't desire redemption. At all. BUT..... The demon lord may be using the character to win over the sympathy of some good-aligned organizations in order to undermine them. Like, maybe there's a temple to a lawful good deity, and the DL sends the character there saying that the DL is seeking redemption so that the temple will accept and help the player, because the temple thinks they're getting an edge up on the DL when actually it's the DL who is playing a long con to use the character to slowly gradually turn some of those lawful good temple-goers away from the lawfulness and the goodness. 

Demons are chaotic. That's their thing. What they say they want is never what they want. There's always a catch. There's always an angle. 

To answer this question you need to know WHAT causes them to be this evil. Demons are formed from a soul becomes subjected to an unbelievable amount of torment driving them almost brink of insanity while their bodies being formed and then suddenly releasing them into the abyss where they'll have to contend with almost every other demon. Of course the stronger the demon the faster they scale up through the demonic ranks while also being corrupted by dark energies of the realm itself.

Now back to your question: I say, a method of doing it that a demon was somehow saved from that tormenting process to become a mad demon and then released into the material plane. There, the demon may begin lashing out first at everything until it calms down, it may encounter a mortal that takes pity of it and slowly teaches it how to be good. I'd avoid using celestials as they tend to kill demons on sight regardless of the demon's state, also a risen demon maybe too much of an enigma and might even scare the celestial causing the celestial to attempt to kill it anyway. Now, you may say, but i was talking about a Demon LORD not a regular demon, in which i say: By regular lore i don't think it's possible for them however a demon that became good and attain power equivalent to a demon lord through it's life is a more likely scenario. 

Note: Most of my info is a mix between what i read from wiki, seen on youtube and i believe some of it came from the demonomicon (an old dnd book). Like, most would say: work with your DM (if you are a player) on this to get what you both find better for the setting.