Draven help

I've been playing him for roughly 3 months now and he is my go-to ADC at the moment, but I seem to be having trouble against a few other ADCs, namely Cait and Lucian.
Lucian somehow outdamages me early game and is mobile enough to make me lose axes/put some burst on me and back off before I can damage him.
Caitlyn is just a little bitch who pokes and pokes and whenever I try to go all in there's a 90-Caliber Net and it turns around in her favor.

Are these just bad matchups for me, or is there something more I can do?

Outplay, outplay. Lucian is highly reliant on landing skillshots to supplement his incredible damage from his passive, which means that without a blink, it's mostly just timing Draven's W to juke Lucian's Q and W. It's a pretty brutal matchup, especially if Lucian has a poke heavy support. Both Draven and Lucian are strong lane bullies, and the only thing you really have up on Lucian is that he can't dodge your axes.

For Caitlyn, she's...a bit problematic. She is extremely safe and can poke you very safely. Consider just farming hard and working towards Doran's Blades or a Bloodthirster for sustain to shrug off her poke, and only go all in if you have a support that can actually lock her down. You will outdamage a Caitlyn in an even fight early game, but her ability to kite and get out of both your range as well as minion aggro range is what makes her irritating if you try to all in her early.

They are both pretty hard matchups for him, since Draven likes to bully early and out-trade weaker early AD Carry champions. Consider checking out this page, specifically the AD Carry section. They might know things that I didn't think of mentioning here.
http://www.winyourmatchup.com/

catch ur ackes

Oh man, this was back when Lucian was first out. Yeah, Draven stomps Lucian early now, especially with something like Janna support. Also I guess don't necro stuff when it's this old and it's no longer relevant, haha.