Arcane Comet can be difficult to land reliably, but the root from Lux's [Q] and slow from [E] make it far easier.
WhyThe Ultimate Hat
If you're able to get a kill with your ult early in a fight, enough CDR could result in you getting your ult back before the rest of the fight ends.
Like most mages a large portion of your damage comes from spamming abilities with CDR.
Scorch is a great source of reliable lane harass damage that adds up over time to build kill pressure.
Lux's biggest weakness is her lack of mobility and proneness to getting ganked. Perfect Timing cna come in clutch if used well to avoid damage on an incoming gank and will provide a reasonable gold value toward your 3rd Item Zhonya's.
More cooldown reduction is nothing but pure bliss for Lux. Cosmic Insight get even more value if you build Zhonya's.