I think an au where Angel Dust and Alastor knew each other in life would be kind of funny. Let's say Angel died at 37 and since every source I found said he died in 1947 that would make him around 22 in 1932.
As for how they'd meet, full disclaimer, I do not know how organized crime works so I'm going to pretend it works like a business and has branches. So let's say that he was sent to make sure a branch near New Orleans was staying in line and not trying to break away but things go south. Anthony/Angel gets attacked and kidnapped as soon as he steps foot in the area and Alastor happens to see.
From Alastor's perspective a tourist just got snatched up by the local mafia and it would look terribly suspicious if he stood around and did nothing, so he goes on the hunt. Through series of hijinks he gets an unconscious Anthony into a getaway car (the driver is one of Mimzy's girls that stuck around) and engages in a car chase that does include guns until the last of their pursuers goes off the road. They end up bringing him to a hospital to get treated for the injuries sustained.
Pro: Alastor gains a life debt that will become relevant.
Con: Angel takes the life debt very seriously and Alastor Does Not Like It At All.
Added lore: life debts are more powerful than soul deals because they're backed by both Lilith, and Eve. If a soul deal brings harm or could bring harm to the person owed the life debt, the contract will be dissolved as soon as the debt is realized.
Anyways, somewhere between season 1 and 2 Charlie does a bonding activity with the main cast (Lucifer included because funny) that includes everyone's first memory of someone else in the room from their perspective, thoughts included.
Everyone goes until only two are left, Angel's first memory of Alastor and Alastor's first memory of Angel.
Angel's perspective is fuzzy because of the combination of drugs and concussion, though it isn't hard to tell what's happening. And the last thing he thinks before passing out is "Mom?"
Alastor's perspective is much clearer, they see Angel getting kidnapped and Alastor coming to the conclusion that rescuing him would be an immoral thing to do because it would 'benefit him'. One of the lines in his internal dialog is "It's not like I'm capable of being a good person, so everything I do must be self-serving." They see him crossdress and use the tricks Mimzy taught him to find out where the local mafia takes their hostages and use his other skills to get in. It does include him knocking out a mafioso and wearing their clothes to gain access. They see him smuggle Angel out but someone discovers the unconscious mafioso and sounds the alarm. They see the car chase and Alastor shooting out tires and drivers when he can. They see him stay in the hospital until he's told Anthony is stable. The memory ends with Alastor thinking "Of course I'm not good. A person with a shred of virtue would stay until he wakes up."
Effect: Because of the realized life debt, Angel's hypnosis is broken, and the boost of power granted by it dissolves his contract with Valentino.
End result: Alastor gains a trigger-happy guard spider that he Did Not Ask For. Eventual RadioDust.
This got really long, sorry about that. I just wanted to get this all out at once.
Except - the reason the life debt is stronger has nothing to do with Lilith or Eve, cause I don't think Lilith has anything to do with deals in canon - its just an aspect of the soul/magic. Of course willingly saving someones life, possibly via endangering your own, is stronger then a contract! And Life Debts have to be willingly acknowledged to fully settle in, but once they do - whoo boy.
(Also, I fully believe the issue with Angel's contract with Val is actually pretty easily broken, that he can just quit - his problem with him isn't the deal. It's the abuse and the difficulty of escaping an abusive partner, and also about the abuse of sex workers. So maybe, rather then dissolving his deal with Valentino, it gives him the strength to quit? I just...I hate Angel being 'rescued'. I think the point of his story is to rescue himself, cause you can't save someone from an abusive relationship, they'll just go back to him. They need to realise its abusive and LEAVE.)