Note: I'm atheist.
You can take the general approach of god created free will and Lucifer threw a fit about serving humans and allows him to live to tempt humans. This is legit but this doesn't answer the fundamental question of first, why god would create Lucifer knowing he would behave this way, secondly why god doesn't correct it, and finally why god would behave so childishly.
Personally, I think there's a much more rational approach. Albeit a bit too romantic.
God can never forgive Lucifer and Lucifer can never forgive God because unless things are exactly so the machine god built will break.
The problem, as I've always perceived it is simple. If you ARE Love, how do you experience love? If you're all powerful you can make anybody do anything you want. If you have that much power, nobody can love you. They might THINK they love you...but they don't. They love your power, they love what you are, but they don't love YOU. The only way to ever experience love from that position is to not use your power no matter how much you desperately want to. Then, and only then, might people say, "Hey...that guy...I love that guy. I don't have to love that guy. But I do."
Now, the question is if that is enough? Not really. It's not hard. You can set everybody to "love" then stop using your power. Boom! But they're still drones. You need them to have personalities. You need them to have a full range of emotions from jealousy, anger, lust, happiness, sadness, etc. And beyond that, you still realize that people might just default to you...you have the advantage. You've had thousands of years and people were MADE by you...there's going to be some bias there. So, Lucifer. Your favorite creation you send to sew seeds of distrust and hatred because you being all powerful realize it's the only way to make things bad enough for humans to doubt you.
So, you can't forgive Lucifer because the machine runs on you two being opposing forces. As soon as one of you stops...everything falls apart.
To put it in even more human terms. Imagine a person you love more than anything in the world. Now imagine one day you find something that'll destroy their entire personality and replace it with just a worshiping shell. Their body is present and their mind is present but no pain, no fear, no sadness, just joy and worshiping you. Does that person still exist or did you kill that person to replace them with a mindless worshiper? Would you feel good about that? Or would you cry uncontrollably realizing you'd just killed the one person you loved to create a slave?
Now imagine that times billions. That's why god can't ever reconcile with Lucifer. If the machine he built breaks through reconciliation all of that vanishes. There is actually something tragically romantic about it. Lucifer must hate his father and humanity because if he ever stops then humanity...the thing his father truly loves...will cease to exist. So Lucifer suffers for eternity. And God...he's perpetually watching everybody suffer over and over again knowing that he's completely powerless to help because in exerting his power...free will vanishes and with it their souls.
As I said, overly romantic but I feel it makes more sense of the general doctrine of God can make everything happy but chooses not to because he's basically a jealous infant.