Lux is one character that have great range on all of her attacks. If one think about it, what if she can use them many times as the player want while doing massive damage? This build is the solution to that. While ignoring the fact that some may have high magic resist. The raw power of this build will still do large amount of damage regarding the opponent's defensive stats.

Lets say if you manage to get Mejai's Soulstealer to stack 20. You will reach over the max cool down of 40%. You may think is a waste to even go over but it is not. Mejai's Soulstealer also increase Your AP by large amount and that itself is a great boost. Without the Mejai's Soulstealer's cool down, the cool down is 34% with the mastery of 4% cool down so the book is not necessary for it to stack to 20 but it does help.

At the same time, you may think that Lux will die really easy since it almost have no resist or armor but that is wrong. When you have Seraph's Embrace, 25% of the max Mana (2789.54) will give you almost 700 HP worth of shield. At the same time, having this build and using Lux's Barrier will give you 365 shield twice. If you can complete this build and use the shield and barrier effectively, you can take extra 1430 damage.

If you wonder why getting the Rabadon's Deathcap so late in game, the main reason is that the Mana and item will consume time. Item like Archangel's Staff which can turn into Seraph's Embrace will take at least 20-25 minutes for it to transform. Also, the amount of money you get late in game increase by a lot over time so getting the super expansive Needlessly Large Rod will be easier too.

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As for the no Boot set, it cost a lot more money and it should make sense why getting Kage's Lucky Pick first. While it adds some AP to help do a little extra damage, it can help you getting money a tiny bit faster. The reason why not getting Morellonomi early is because it does not do significant damage unless they have more HP. It may look like is the same thing but it is not. when you apply the effect on first hit, it will do 5% damage of their HP at the moment when it hits over time. while is damaging your opponent, using other attack will reduce their HP while that 5% damage still apply. If you do it fast and they some how live through your combo. that little left over HP might get destroyed by the Morellonomi.

Skill Sequence of this build is easy. Due to the fact that you have such crazy amount of Mana,
Mana Regen, and high cool down. You can engage combat from far with Final Spark. Finaly Spark with some deductions, it should do at least around 700 or so unless they are AP tank. When they are close enough for your regular spell to hit. While you are moving carefully and looking for best time to snare with Light Binding, your Final Spark should be ready to fire again. Using Light Binding+Lucent Singularity+Final Spark will do massive amount of damage.

First using Light Binding to stop your opponent. Then use Lucent Singularity directly on your target but DO NOT detonate it yet. As soon as you fire Lucent Singularity, fire your Final Spark and then your can move towards your target to do at least 1 normal attack. While detonating Lucent Singularity may give you a chance to do 2 normal attack with Illumination. The order will be like this, Binding Light->Lucent Singularity->Finaly Spark->Normal Attack->Denonate Lucent Singularity->Normal Attack. Lets say if all 3 of your spell hits that target and both normal attack hit while illumination is on them, the set with the Boot will do around 2700 of raw damage and the set with Morellonomi will do about 3200 raw damage. With deduction from the target defense, it is most likely to do at least around 2100 or 2500 average damage to your target. If you add the 700 damage from before, it is around 2800 or 3200 total Damage. Not many champion can survive this much damage unless they have a lot of defensive item.

Pros
High Cool Down
Large Amount of Mana
Great Ability Power
Can shield large number of hits
Can kill tanking champion easy
Very hard to run out of Mana
Very strong once game reach 30-35 minute mark

Cons
Not alot of HP and defense from stats
Hard to fight against fast moving ADC
Can be hard to play at early match