For some reason, I've had way more success playing Lux as a botlane support than a midlane mage.
Her Q is a 2 second snare at rank 1 that can also snare a secondary target for 1 second. It doesn't scale in duration like Morgana's Q, but Lux has way more burst damage and poke threat (especially early on) than Morgana ever will (her pool doesn't do a lot of damage and Morg's base attack is actually pretty low). Landing Q into a right click on the enemy ADC will incidentally proc all 3 stacks of spellthiefs (the passive explosion counts as a proc).
Her W is a nice shield (though usually I either whiff it on a dying teammate, or they run away from me even though I could have saved them had they embraced my protections). Unlike Orianna, it's aoe, and refreshes twice. It's nice for tower dives.
Her E is a nice slow. It's also a great bush scouter due to it's long range, fast travel time and large sight range. It also adds to her burst damage and can function as aoe damage later on for pushing minion waves. I really like the utility of this spell.
R is great for securing kills that have "gotten away" and the base damage is very high.
For some reason I never have mana issues as support lux, but always run into the mana gate as mid lux. Also for some reason whenever I run mid lux, 75% of the time it's Yasuo/Zed mid.