Just looking for some real tips on how to counter 
in lane. I'd rather not be forced to hide and cs under turret just because a summoner learned really good and can catch axes doing that extra damage every shot, I don't have the mana to just throw at him to punish for catching that axe over and over. Any tips so I can stop cowering?
first you support or adc? second do you have cc? 3rd general tip, if he catches his axes then you know where he will be standing, if your a 
He's fucked.
He's oppressive in low elo imo cause bot laners usually don't understand how to trade against him together.
I think Cait can work, if you utilize max range while he's going for CS. You just have to be very very careful about his hard CC and his support.
You won't necessarily have to farm under tower if you keep the wave even while majority of the time closer to your side for safety.
Your range can potentially beat him once you reach BF sword, his IE spike is a lot more than yours imo though. So you only have specific windows to abuse him with your range.
But your traps and E also do well with keeping Draven down.
But TBH, life steal + warlords draven is just a little too nutty.
Draven is good in lane though vs low elo players, since he pretty much outdamages and punishes each and every death with his passive and insane damage. He can just go to pound town if he has decent awareness and mechanics with Draven.
Depends on the champion you have. Personally I take Caitlyn into Draven simply cause when he pops his W to go in for a trade, I can minimum EQ auto to chunk and possibly dodge his damage. If you are really good, you can even WE auto Q auto (if the trap catches) for an even better trade. Granted, you are trading a lot of mana to counter his engage, but it's something.
The other thing is look at your minions and trade when he's going to go for CS. If his axe is going for a minion, it's going to be a second or so before he can turn on you.
Varus is great against him along with hook supports like thresh and blitz anyone with a counter engage is great leona is particularly good as a support once he has BF sword though you can 1v1 him unless your fed his power spike is insane with bf sword so watch out
