Playing AP Lux build, your default rush is Luden's Companion. In cases, when an enemy team is full of tanks and HP stackers, go Liandry's Torment.
Adapt to an enemy team. Are they full of tanks, and they rush tons of Magic Resist? You rush Void Staff as #2 or #3 item to counter MR stacking. Their team has champs with lots of healing? Rush Oblivion Orb as #2 item (upgrade to Morellonomicon as 4th or 5th item).
Somebody is going after you each fight? Always getting ulted by enemy assassins? Rush Zhonya's Hourglass.
Tips and Tricks
Champion
You can use Lucent Singularity (E) for scouting and bush control.
Lux is great at countering pushes. You can use Lucent Singularity (E) to stop enemy minions from afar, and you can clear them with E + Final Spark (R) if needed.
If you are playing more support oriented Lux, you can be more useful to not detonate your Lucent Singularity (E) instantly - it keeps applying AoE slow triggering Font of Life effect as well as items like Imperial Mandate.
Look for enemies that are hiding behind a single minion. You can catch unsuspecting enemies with your Light Binding (Q) (second part).
Riot
Lux has great zone control abilities. Try to set up Lucent Singularity to prevent an enemy's advance or escape.
If you have trouble landing Prismatic Barrier, remember that it returns to you after it reaches max range. Try positioning yourself to hit your allies with its return trip.
Lucent Singularity is a great scouting tool. Try throwing it into brush before walking into it to check for ambushes.