The idea of this build is to make use of his passive and his abilities. The AP for the abilities when your able to trigger them. The AD and Attack Speed for when your cooldowns are going off. While yes his passive wont trigger again on the same target until after 3 seconds, the idea is to continue doing a great deal of damage. Also with this hybrid build it will assure damage regardless of what they enemy is trying to defend against. Whether it's with armor, or with magic resist.

The reason for the Hybrid is because of Ekko's scaling for his AP damage.

Item Reasoning:

Lich Bane, this one is quiet obvious....
Luden's Echo, while the AP is obvious, but why? My reason is for the movement speed to be able to catch your opponent if they happen to not die from Ekko's abilities.
Beserker Greaves, this is again to boost your speed to be able to chase. The attack speed to land more hits when your abilities are on cooldown.
Phantom Dancer, Again to boost your movement to be able to chase, and to deal more damage when on cooldowns. And with added crit chance to do the extra damage when it decides to pop.
Nashor's Tooth, again.... Speed, and then with that cooldown, and more AP to the abilities.
Hextech Gunblade, this was is optional to fill for defense item. The main reason for this is to utiltize the AD and AP to sustain your health when in 2+ engagements.


Runes:
AP and AD should be obvious by now....
The HP runes are for the extra kick to make Ekko more survivable.
The scaling is because it's not important stats early game, but come in handy late game.


Not much more to say then happy killing
- PhantomGe***