My Lux gameplay is based on hitting combos, doing fast lots of dmg, and saving kills. Also being able to shield and run when attacked to replace me and hit back or flee.
Lux does her work best if she is not close to the enemies, but skill shoots them to death with her fast combo.
Also, she gives you the ability to shield your whole team during team fights giving a bonus during keeping distance in order to wait for cd and hit.
It's really all upon tactical thinking and keeping max distance with your abilities when being chased. From this point, you can't wait till your cd allows you to hit combo.
Most satisfying is at late, when you gonna melt down everybody by just q+r. Having a lot of carrying potential that should not be wasted by playing utility supp or sth. Your team can always need a bursting lux best