Forget all the Lawlight AU's, what this society needs is an AU where Soichiro Yagami is not dead.
Soichiro was a good person and always did the necessary for justice’s sake, and at the same time, he was loyal to his family; even when his son was accused of being Kira, he still believed that Light was innocent. He deserved better.
Instead of dying, Soichiro goes into a coma. Again, Light does his lame act of being a innocent guy who lost his father.
It takes some time for Soichiro to regain consciousness, and when he does, it's been months after Kira was killed. The task force, while still being angry/heartbroken thanks to Light, goes to say hi; they never expected for Soichiro to ask about his son so fast.
For a moment, they hesitate, but before anyone can say anything, Matsuda speaks. He tells Soichiro that Light is dead, but for Soichiro's sake, he ends up lying. In an attempt to protect his hero's heart, he comes up with a lie where Light was controlled by Kira; he also tells Soichiro that Teru Mikami was the real Kira.
Of course, Soichiro can't believe what he is hearing. His son, the son that he loved, the son that he tried to protect with his life, was dead thanks to a psychopath, a murderer. He can't help but to blame himself, thinking that if he was there to help, Light would still be alive. Matsuda tries to convince him otherwise, it's not his fault that Light was another victim of Kira; Soichiro is not convinced, but tries his best to not blame himself (or at least, not blame himself out loud).
Once the visit time is over, the others start to question Matsuda about what the hell was that. Matsuda tells them that he always admired Soichiro, that he was like a father to him; and no father wants to hear that his son was a killer after he thought that he wasn't (aka, when he used the Shinigami eyes). Soichiro is like an idol to him, an inspiration, so that lie was the best way to protect him. The others understood quickly, after all, they also admired Soichiro.
Perhaps, one day, they will be able to tell Soichiro the truth; but for now, they will play the same game Light Yagami loved to be part of, pretend that he wasn't Kira.