I have a lot to say, most of it not so good. But to start with something positive, I like the fact that you have left cc out of his kit (with the exception of a slow) and that he has no mobility. This shows that you have tried to create some tradeoffs with his kit. That being said, there are a LOT of problems I can see; I'll start with his passive and just work from there. Note: this ends up kinda long, but I've tried to explain my logic as well, I hope this long response doesn't scare you away.
His passive is just INSANELY overpowered. I mean, you've basically taken the passive on ekko's W when ekko has 400 AP and said he can use it any time, on abilities and auto attacks additionally without any initial restriction (ekko's only triggers when targets are below 30% health). This is an absolutely MASSIVE amount of damage that will cause him to win trades easily and keep opponents weak with almost no effort. In addition to this, he is healing for the damage dealt? Here is a quick example. A minion starts with around 470 health. If you last hit a minion with 30 hp left with this guy, you're going to heal for 40 hp (9% of 440) With just his passive, you have given him excellent sustain (rivaling chogath) and the ability to out-trade instantly. I don't even think this is a good idea for a passive, its simply too powerful to have numbers anywhere near as high as they are. And I can't even say if there is a number where this would work, its insanely strong. I suppose if the % missing health was less AND it had a cooldown on each target you might be able to justify this ability.
Now his Q. Again, I think this ability is a little overpowered. First, infinitely stacking attack damage is probably too strong a concept to introduce in the game. The only person that comes close to this is nasus, but his "ad stacks" applies ONLY to his Q, a restriction your champion would not have. With every ability scaling off of ad, I think this is something that could get out of control very quickly. Not 100% sure this would be a bad idea, but its a scary concept. If you are trying to make an ad version of veigar, please recognize that ad and ap scale in different ways and what works for ap doesn't usually work for ad. You've also given Mort even more healing on this ability. What? It's too much, especially for a 25 mana cost item (nearly nothing). And lets not forget the passive synergy.
No problems with his W. It feels super underwhelming given how much power his passive and Q have, but that isn't a problem. In fact, its a good thing. Here he has a utility spell that serves as his only method of closing the gap. I even like the bonus ad ration on it; helps the ability not be completely utility based. Wait, you didn't see this, but this was added as an afterthought; this ability procs his passive. Nevermind. Its sorta too strong, but again, I suppose thats a problem with his passive, not his W.
His E seems to me to basically be an ad version of Karthus defile. Not against the concept, but its mana cost seems VERY low for how much damage this ability does. It scales better than karthus E, and is only 40% of the cost. Oh, and it also reduces armor, making it MORE effective. Oh, but lets not forget that it procs his passive also. Yikes. I like the idea of the ability, though it needs some very serious mana nerfs. Or make in an on hit effect (rather than a continuous one). Food for thought.
His ultimate is good. I mean, I think it lacks creativity (no offense intended) but there is nothing wrong with it except that its basically the same as his Q except he gets a dot. And steals AD. Not really that exciting. Its also much too high damage because, again, his passive.
In a quick summary: The biggest problem on this kit is his passive. Its beyond broken in its current form. This trickles into the rest of his abilities, essentially making him completely overpowered. He has too much free damage and too much sustain in his kit to be anywhere near balanced.
I am interested in the lore, etc because this does seem like an interesting concept; the execution is just slightly questionable.