Lucian: Best Build Sequence?

Can someone please help me with this? What are the must-have's for Lucian? I am just not achieving the results I want for The Purifier. I always start out with no problem: 1. Doran's Blade 2. (Boots) Berserker's Greaves 3. Blade of the Ruined King But what then? Rapid Firecannon before or after The Black Cleaver? And why get The Black Cleaver for cooldown reduction, when I can build a Nashor's Tooth and get better attack speed? Is Trinity Force a good option for Lucian? Or is The Black Cleaver is a "must-have"?
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