Whenever someone brings up Lux support I always have to point out that morgana support does everything lux does and more, and better.

Because I'm an *******.

You can also throw the auto attack before exploding E if I'm correct.
You slow them with E > auto attack > E (before the auto attack hits the target) and it will still proc the passive.
This allows for a quick burst and maybe an extra auto attack because they will be slowed again.
I haven't played her in a while so you should try it.

You should mention Mercury's Treads and Ionian Boots of Lucidity. Since you don't take any points in defense, also no points in tenacity, I think they are very valuable for your build because she's so squishy and she can only protect herself with her spells. Lucidity boots should be bought only early and sold later though.

I'm missing special warding places for pinks and sight wards. Deep warding can be really useful. And where you get the most vision from, special spots in bushes.

You should mention why you take or not take Inspiration and Intelligence . I think the reduced cooldown on items is really good. 20% CDR on mikaels is like a half minute.

I think Chalice of Harmony + 2 Stealth Wards + 1 Vision Ward is good when you back and had a rather good laning phase. Running out of mana is horrible with her because you get so easily ganked even with wards. Her spells are the best form of protection in my opnion.

I would mention that she can push the wave with her E a lot and that you shouldn't pick her in a squishy team comp without front line. She lives from shielding from the backline. At least 1 person tanky enough to engage.