Flash and Barrier are paramount to the survival of Lux, whether against Syndra's Ult, Veigar's Ult, against a lot of damage.
This will enhance the protection of your current shield and will help you a lot.
Lux is very squishy at the beginning, so barrier is a perfect summoner for her.
But you can also take Flash Ghost if your matchup is dead and you do not think that you will have any kill, shift to the botlane or to the toplane with Ghost, it will help you a lot.
Flash Ignite is also viable, if you are sure to kill your opponent like Veigar, which is very easy to kill.
Flash Fatigue can help you, but not as much as barrier or ghost, if you're against an assassin, give up, you'll have to wait under turret trying to see an opening, so it's better to take ghost and shift towards the botlane (Which will also offer you 2 kills, a turret and a drake.)