Vlad struggles are more of a gameplay issue than a raw numbers problem.
The upcoming hotfix makes it pretty clear that Vlad's recent update has left him feeling weakish. There have also been examples of him dominating in certain situations, which leads to the dilemma of how to fix his performance issues without giving him even more power where he is already succeeding. Various suggestions have been made, from numbers tweaks to casting animation removal to further reworks, but the root of the problem seems to be inherent in the new timing mechanics and how they interact with the rest of his kit.
Vlad is now reliant on utilizing relatively short windows of opportunity to engage successfully. Unfortunately the nature of the timing involved telegraphs these windows to his opponent, and he lacks the means to force an engagement if his opponent simply avoids him during those windows. From a pure numbers standpoint, if you know how Vlad works, and your opponent doesn't, it's pretty easy to steamroll your way to victory. If, however your opponent understands your kit, they will out trade your two weak Qs, farm or harrass for 5-9 seconds while it CDs, and then avoid you for the short window your empowered Q is available. Attempt to charge your E to even the trade at any point in this process and they will simply back away or CC, leaving you to damage yourself and push the wave, and possibly get some free hits in.
Another timing issue becomes more prevalent in team fights. On paper, Vlad has incredible sustain potential. Unfortunately, with the charge up requirement for his empowered Q, and the delayed healing from his ult, odds are if you really need the sustain you'll be dead before you get it.
Time will tell how far the upcoming numbers tweaks go towards fixing the issue, but it seems the problem is more complex than a simple lack of damage.
Ideas that might be more helpful than just OMG MOAR DAMAGE pl0x:
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Increase empowered Q uptime. In addition to the obvious benefit of giving Vlad more time to do his thing, this places more strategic importance on the opponents decision to avoid him, effectively zoning themselves out for a more meaningful length of time.
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Increasing the duration/power of the speed buff. If your opponent is paying attention to your timing, they can start backing off before the buff even procs. A better speed buff would give a better chance of closing the gap, again forcing your opponent to make a more meaningful retreat if they opt for avoidance.
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Frontloading a portion of the heal on his ult. Better sustain in teamfights while you wait for that empowered Q -Half immediately half on explosion. -Heal-over-time for the duration -damage based drain a la Hecarim
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Reduced visibilty for his E. Have it fade in as it charges, giving a better chance to catch them unaware. Not a huge difference on its own, as the charge happens fairly quickly, but arguably useful as a package component with other minor tweaks.
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Some type of benefit for Vlad if his opponent opts to avoid his empowered Q. Something with more strategic value than simply wasting it on a minion. -Refund a stack -Combine with one of the other suggestions and increase the duration/speed of the next empowered Q
In short, Vlad in his current state is just too easy to counterplay.