You may ask yourself the Simple Question:

How is this build supposed to be viable?

The simple answere is: it isn't, seriously, you are loosing out on so much potential DMG!

But nonetheless, it is still possible to make it work.

Our Core is quite Simple to explain.
Lich Bane is a strong first pickup, as Your is at the same time an on hit and a ability when it comes to how Lich Bane treats it, other items don't treat as an Ability so it becomes tricky very quickly! But Lich Bane's damage makes the early game still work out for now.

Your second pick up is Luden's Companion as your can Trigger it, along side your Ult , there is a small work around to make Luden's Companion Proc on your , and that is the 3rd Item of our Core. Stormsurge's Passive ability Squall gets triggered by dealing the enemies 25% max hp in a matter of 2.5s, with a cooldown of 30 seconds, meaning it doesn't matter what ability got used to trigger it's effect, it can be triggered even from something as simple as AA if the DMG is high enough, and Stormsurge's Squall also counts as an Damaging Ability, meaning It can Trigger Luden's Companion and vice versa.

Now to the Elephant in the Room:

If we give the benefit of the doubt, and say you will with all 3 Items Lich Bane Luden's Companion and Stormsurge trigger in One , that DMG without extra Items (and without getting affected by the rune choice) will Deal around 800 DMG, AT LVL 18.

In Comparison, a Yone with ONLY Blade of the Ruined King will Deal around 400 DMG in the same setting, that being a 2 ITEM DIFFERENCE

adding Infinity Edge and Immortal Shieldbow to make it a fair 3 Item comparison, His will deal around 900 DMG, this difference may not seem as drastic as i say it is, but thats until you start to consider, that Luden's Companion Has a 6 second cooldown, and Stormsurge has a 30 Second cooldown, Emphasising on how much DMG you will loose out on.

The reason why I'm explaining the difference so deeply is because I want any person crazy enough to try this build out to be aware of how much more struggle they will have to make it work!!!

I tested out Some theoretical last Items, for example Shadowflame, but because you will have a hard time on your own to get enemies low enough to benefit off it, Going Double burn seems to be the best option here when it comes to using your Item to the fullest, though switching Blackfire Torch for Rabadon's Deathcap Will Increase your DMG but decrease your DMG a bit, If you ask me, I Would rather go the Rabadon's Deathcap Route as the extra DMG on your is just too good to pass on when you have it every 2 seconds.

This build gets countered by almost anything, as it will be hard enough to get your core items in the first place, once you have it you can start to participate in more then just setting up plays for your Teammates. but before that, you are a glorified support laning on either top or mid lane, you either need to play with your team alot to properly use your DMG, or have the luck of having 2 winning lanes (as yours probably won't win) and because of that, having weaker enemies you can have fair fights against (despite you being in an item advantage in that case)