As a Lux main (I actually just posted a thread about possibly buffing her because of how easily she can be countered) I'd be happy to give you some pointers/things that can be difficult for a Lux to handle.
1.) Play to her cooldowns. Lux, especially very early, is EXTREMELY cooldown reliant. Depending on the champion you play, consider getting boots with alacrity to help you dodge/reduce the duration of her snares (merc treads work nicely). If you see her toss out a spell, and she misses it, - right after she misses it for about 10-13ish seconds she becomes extremely vulnerable. If you play a champion with a higher movespeed, take advantage of her extremely slow early MS.
2.) Fancy feet are required. Watch how she tosses her E, and learn to 'bait' the spell. Always stay behind 2 or more minions if you want complete protection, as her Q will snare two targets.
3.) Use your flash wisely. Flashing out of her ultimate can leave you with every one of her spells on cooldown, leaving her in the most vulnerable position possible - as she'd have, with no CDR, a full 10-13 seconds before she is able to hit you with another ability, - and the laser's CD is long without cdr.
4.) Keep an eye on your 'illumination' debuff. Not letting her autoattack you, or baiting her into a vulnerable position because she's trying to auto you can work to your advantage, and can be a definite play for you + a jungle to make a gank. Oftentimes as a Lux mid, I might overextend just to get the proc on the illumination debuff for extra damage, - but of course this often means I leave myself in a tricky position if the enemy jungler is nearby.
5.) MR and Zhonyas are your friend. Zhonyas can make a Lux ultimate worth absolutely nothing, and adding a bit of MR into your build (depending on the champion you play the build would vary) will make her spells a lot less effective - and force her to build items with penetration rather than pure damage, thereby potentially weakening her. If I see that a champion isn't building much MR aside from maybe an Athene's, - I oftentimes will build pure glass cannon and turn myself into an artillery gun.
The biggest points to master are number one and number two. Remember that her spells early leave her very vulnerable if she misses any of them. Being able to dodge and bait her is key, because she has very little MS - and if she is caught out of position, she is very vulnerable.