Yes, he definitely needs changes, though right now he's not prominently annoying enough to warrant a high-priority rework for the time being. His passive is boring, his Q has frequently been cited by Riot themselves as one of the worst-designed abilities in the game, and his E is also not really rich in choice or interesting gameplay, both for him and his opponent. On top of that, his health costs quickly become irrelevant once he gets spell vamp, which doubles down on his free healing and is still one of the reasons why the stat can't be made good on more champions.
Personally, I think he should have potentially much more powerful sustain, as well as even better anti-group damage (to me, his niche feels like that of a mage who likes to vamp off of as many enemies as possible by catching them in his spells, particularly his ultimate), but he needs to be a lot riskier than he is now to achieve that. Currently, Vlad's laning pattern just has him hanging back and free-poking the enemy laner until they either lose out of sheer attrition, or manage to get a lead from a hard gank and out-trade him from then on, which makes for really uninteresting, often frustrating, matchups. It doesn't help that he gets tankier from building damage, and vice versa, as it makes lane matchups even more snowbally in either direction (either he gets to out-tank and out-DPS his opponent at the same time, or he ends up flat-out weaker in all respects).
Thematically, I think it would be kinda cool if Vlad used other people as part of his own circulatory system, pumping them full of tainted blood before sucking it out of them to heal himself, and perhaps deal even more damage to them too. In gameplay terms, it could amount to him losing out on his on-demand free healing, but instead have his sustain scale with how hard he commits to fights, with his healing and damage scaling super-hard with how many spells he chains onto his targets. Given the proper amount of risk and difficulty, he could afford to have even lower cooldowns on his Q and E, which would tone down the awkward gaps in his DPS and synergize better with his ultimate.