His laning is actually not that great at first. His sustain is weak, every ability besides Q costs him health and he's a mage so his auto attacks are meager. Champions who perform well against Vlad are the snowbally ones who can go aggressive on him early and HARD and then force him back at low health, then zone him from creeps for as long as possible. If he can't get near creeps, he can't heal himself and he'll have to b. If you're jumping on him, then pushing lane to his tower you're making a mistake. Vlad farms well under tower and the creeps will heal him besides.
To beat Vlad in lane you have to starve him. Try early game yolo powerhouses like
,
,
,
, or
. Go in on him as early as you can and go in HARD... then just do all you can to zone him away from creeps. He'll eventually be very strong, but you can delay it as much as possible. If he pools to avoid death and then comes back to try and sustain off of creeps (which you should be keeping WELL away from his tower) then all-in him again immediately. Unless you're super low yourself he'll die with minimal fuss and every time he does he'll be less and less able to survive your brutal all-ins. Just remember to get lifesteal early so you can heal up from your trades with him, since you're melee and will likely take some minion aggro when you spank him early.
This spoken as someone who plays Vlad. When in doubt that is the best way to learn how to beat a champ. Pick him up yourself and see what sorts of champs, strats and items give you a really hard time. Odds are, it's something that will thwart other players of that same champ too.