after u build the Vampiric Scepter you gain an even higher sustain plus u can fight the enemys now with Sheen and lifesteal.
You could also Enchant furor but i would recomment Alacrity because your movment speed is very low.
The Deathfire Grasp doesnt give you ad but based on the fact that all your abilities deal magic dmg u increase your dmg output by 20%.
You might change the Infinity Edge to a Warmog's Armor but you get very much hp with your passive and your lifesteal.

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your Mace of Spades is your main dmg skill in late game because it's your only skill that scales with ad.

Your Creeping Death gives you some sustain in the fight and healps you farming if your hp is low and your enemy is ranged or is a burster.

Your Siphon of Destruction is your farming skill it does very much dmg even without ap.

Your Children of the Grave can change fights very easy and it gives u health back even on ad you heal for the ammount of dmg ur ult does.
When the enemy who gets ulted by you dies in the time your ult is active you gain a ghost.
The ghost gets a percetage of your stats and you gain a percentage of the ghost stats.

I would recomment to use Ignite and Flash as summoner spells.
Ignite pushes ur ult and makes it nearly impossible to survive if they are under 30% hp and u ignite them while u ult.
Flash is just a very usefull skill to close gaps or to run away. It can save ur life more than once a game :).
you could also use Ghost for mobility but i recommend Flash because you can shorten the ways or be a little trixy.

-pros
*high sustain
*strong burst
*strong dot
*hybrid dmg
*incredible strong late game
*easy to get tripple while in GA

-cons
*if CCd you die
*no slow/stun
*weak agains burster
*weak early game