My favorite lore for aasimar is the big question of "What do you do when the world expects you to be perfect?" It goes like this:
Mortals were never meant to go to the outer planes. They're beings of flesh, bone, blood, substance, elements. The outer planes aren't good places for things of substance. Out on the planes, the food you eat is grown from seeds tainted with ideologies, in soil made of microbes with morals, from rain brought by beings of chaos or order. A mortal can live on the planes (well, in certain parts of certain planes, anyway), but life out there changes you, especially over generations, to someone with planar energies
in your substance. Your blood has water that might have once flowed in the Styx, your bones have calcium from stones hewn by the gods, your lungs are filled with the numinous clouds of infinite heavens. Over time, people who live on the planes may give birth to planetouched. Tieflings, aasimar, genasi, etc. - these are people (humans, in those cases) who are literally touched by the planes. Most planetouched are born unexpectedly, to parents who are otherwise fairly normal humans, so they don't really have much in the way of independent society. Two aasimar who have kids won't make an aasimar baby. There's no tiefling empire, no genasi village. You could have an ancestor that's a fiend, but you could also just have an ancestor who did a stint in the Nine Hells and in nine generations, you got a tiefling. It's fantasy logic, not biology.
People being people, and the planes being what they are, there's stereotypes. Tieflings are mistrusted, because evil is
in their physical forms. They come from places chock full of evil people, where the air and the soil are born of solidified evil. It doesn't matter if your parents were a paladin and a saint, if you were born a tiefling, people are going to have a hard time trusting you, because evil
makes you. Of course, the truth is that you're able to choose your path in life just like anyone else. Being a tiefling doesn't mean you're evil any more than being left-handed. But people are people. Just look up the origin of the term "sinister."
Aasimar are the other side of the good/evil coin. Good is
in them, in their blood and bones and breath, in their physical form. Just like a tiefling, your choices make you who you are, but Good is in your
substance, and people are people. So you're seen as a favored child, a child of destiny, a child chosen by the gods. Even if your parents were pig farmers, now everyone thinks you have a
destiny. That you're supposed to be a hero. That you are capable of miracles.
Of course, there's not necessarily any truth to that, and that's where the interesting character dynamics are at play. While tieflings have to struggle with the assumption that they're baby-eating bogeyman (regardless of what they are), aasmiar have to struggle with the assumption that they're somehow more perfect than they really are. Some aasmiar absolutely take advantage of that - petty princelings and self-centered god-emperors who sit on gilded thrones or enjoy the sycophants around them aren't unknown. Some aasmiar struggle more with it - with being flawed people expected to be perfect, with the pressure of having to "save the town" when there's no way to save it, when the forces crushing it are too big or too abstract for one person (and aasimar are still people!) to handle. Others do manage to live up to the reputations, to be the heroes that they are expected to be. Or, somehow, to be the heroes
they want to be, regardless of what the world expects of them.
Aasimar characters with this kind of lore struggle with the burden of great expectations, with the assumption that you're going to be a noble and true hero in
someone else's eyes. You're alienated from others because they see themselves as unworthy of you, they see you as better than them, they see not who you are, but what they believe you to be. You are put on a pedestal, one that is shaky and unsteady, but not one you asked to be put on. Can you define who you are, or are you going to be defined by others? Can you be the hero you want to be, or the hero they need you to be? Are you a people-pleaser? How do you use your privilege? Are you a disappointment?
This kind of lore is very
Planescape-coded, in that it's about how belief doesn't always line up with reality, and in that it's about how you make an identity for yourself out of these big, cosmic ideas that are swirling around. If the world sees you as a Good Person, just because of how you were born, how do you deal with the inevitable guilt of not being enough? I also like that this lore can produce entitled, self-absorbed villains who are entirely too confident of their own correctness, and that those villains can rally otherwise well-meaning people around them ("Look, I know Hilda The Eviscerator is a good person, because just look at the feathers in her hair and the sparkle in her eyes!"). I also like how it works with tiefling lore, and how these two bits fit together to make two different versions of the "birth is not destiny" story. I like to imagine a party with both a tiefling and an aasimar, neither one quite what people would expect, both of them able to play the normies off each other with their narrowminded assumptions.
The "conservative" religious version of some angels tends to be unappealing − either too sexist, homophobic, dictatorship supporting, etcetera.
The Lawful Stupid Paladin ethics are unappealing.
The elevator-music goody-two-shoes is boring.
The fallen angel, including the angel becoming flesh, is a tired trope. A flavor that rejects what Aasimar culture is, offers less information about what that culture actually is. Also, the angels as flesh, sex with angels, and misguided attempts to return to the Garden of Eden come with objections from various reallife religions.
I think the lore I like is kind of close to the last one here, but the emphasis is on how celestial beings are seen as perfectly good, altruistic, benevolent beings, and how you - a mere mortal with pretty eyes or whatever - are also expected to be a kind of that. If everyone thinks you're god's gift to mortals...well, what do you do with that?