Hey, I did a quick search on Lux on both Reddit and the Gameplay section of the boards to see if any recent posts were made about Lux as a support, and from a cursory glance, I didn't see any.
From a purely kit standpoint, I feel like Lux is too oppressive in bot lane. Off the top of my head, the main hook/root/stun champions commonly played as supports that have reliable immobility CC are Morg, Blitz, Thresh, Leona, and Naut. As far as I can remember, most of these other champions can easily be minion blocked, making counterplay much easier. I'm not sure if Lux being an excellent support was a design goal or a side effect of her CC heavy kit, but I think that low cooldown ranged roots that can punch through minions along with slow bombs feel too strong in the arena of bot lane. I don't think Lux as a midlaner is particularly awful; she's certainly not a favorite matchup, but it's definitely a lot easier to play against only one champion vs in bot lane where CC is (I'd argue) more prized as an engagement setup.
Is this just my garbo skills talking or do I have a reasonable point? I think Lux is far too strong of a support (sorry, but a Taric vs a Lux in terms of CC and poke ability, is it even a comparison?). Is this even a valid position to take? And if so, how would she be tweaked without killing the very nature of her kit? I want to be clear that ideally, I'd tweak her rather than rework her kit entirely.