This particular Lux build focuses specifically on cooldown reduction and ability power; Lux has very good survivability skills if one is a careful player.

If the enemy team has a lot of stuns, snares, or disables, it is worth it to get Mercury's Treads instead of Ionian Boots of Utility or Sorcerer's Shoes. Late game you don't HAVE to sell your Ionian Boots of Utility for Sorcerer's Shoes; you do enough damage for it not to matter too much. However, you can if the enemy has lots of magic resist. Rylai's Crystal Scepter is a very end-game item; if you need the health and the enemy team has champions that have speed boosting abilities, it's a must-have. Otherwise get Lich Bane or another Archangel's.