What sin was Beatrice based off?

We know that is gluttony and is lust, which leaves envy, pride, wrath, sloth, and greed. The demons usually take on an appearance suited for their job (Tahm's mouth/size and Evelynn's attractiveness).
I'm not sure what a raven would signify, but her many eyes could represent envy, as she'd be able to look and covet more things at a time (just grasping at straws here).

There's also the manner of how/why she would give him power. We know that the demons usually lure in their prey (with a promise of some sort) which may mean that Beatrice attempted to lure Swain (possibly with the power/vision to reclaim Noxus) but failed, resulting in Swain overcoming her due to his strong will (or maybe she's just giving Swain the illusion of power).

It should also be noted that the demons usually have to wait to get the maximum effect of their CC on a single target (Tahm's Passive, Evelynn's Allure) which may indicate Swain may have taken over, it may mean that a demon having a host removes some of their limitations. His Vision of Empire (W), however has a delay, but is free casted and AoE, and gives vision rather than CC which may be the result of having said host (or one of Beatrice's perks).

While we're at it we can talk about the eventual lore change for after his eventual rework. I think they'd probably make him Wrath.