Here, I'll try and describe some of my strategies for playing against other common mid lane champions. Again, take this guide with a grain of salt; all games are different, and all situations are unique. Sometimes you may need to deviate a little from your regular playstyle in order to make the most of a certain situation, that's perfectly fine. The best players are able to mold their build and playing around the current situation, but this matchup section will help you get an overall sense of laning mid Lux.
Ahri's can start out pretty passive, but she gets scary when she hits level 6. Poke her as much as you can while staying out of charm range. If she dashes at you, attempt to bind her. If you connect, try and finish her off ASAP. Blow everything, your ult and ignite if you have it. You need to get it off quick because as soon as the bind runs out, good luck hitting her with your skillshots. If you miss the initial bind, back off immediately, taking care not to get charmed. Ahri likes to roam often, so when you see her leave, make a quick decision to either follow, or start pushing the wave immediately. If you push every time she leaves, her tower will go down quick and she won't have the luxury of roaming anymore. If you follow, try and stay out of her sight so that you can counter-gank effectively.
Akali is another champ that usually plays pretty passive until level 6. Use your range advantage and autoattack her when you can. If she Qs you and then runs towards you to proc it, kite with a snare and turn around to pop your passive on her. If she likes to hide in her shroud, throw one of your Es in and pop it in the middle. The radius of your E is almost as large as the shroud, so you have a good chance of hitting her. If you get jumped on by her ult, snare first, then start retreating and regain your range advantage.
Anivia is a pretty good matchup for a Lux player. Early on, harass often, especially if her stun is down. The cooldown is long, and spamming stuns takes a toll on an Anivia's early game mana pool. She will try and push you when she gets level 6 and has blue buff. Push back with your E+Autos because Lux is not a good last hitter under tower. If you have the opportunity to burst Anivia down even when she has her egg up, DO IT! The egg is a 4 minute cooldown, your ult is a fraction of that. It's worth using your ult to get Anivia into egg form, just be aggressive again once it's up and she will die.
Annie is another good matchup for Lux if you play right. All of her skills are lower range than yours, so use that to your advantage and poke with your E when possible. She will probably try and autoattack you often with her 675 range, try and turn on her when she does and you'll win the trade with minion aggro in your favor. If she runs at you with her stun up, calmly snare her and back away. If you get a Tibbers dropped on you, don't panic, just shield yourself and walk away.
A good Brand player can be troublesome because the range on his Pillar is pretty big. Brand is very reliant on comboing his skills however, so if you get hit by one, back off until his Blaze passive runs out. Stay away from minions because they can serve as extra bounces for his ult, and if he Conflagrates a minion affected by his passive, it will jump to you.
Playing against a Cassiopeia requires a lot of micro and juking her Q. Try to not be obvious when you are going in for a last hit because good Cass players will Q right where your champions runs to. If you do get hit by the Q, shield yourself and quickly get out of range or her barrage of Twin Fangs will hurt a lot. Cass with blue will probably push you as well, so either push back just as hard, or steal her blue with help from your jungler.
Fizz can be rough as a Lux player because his Playful/Trickster makes him untargetable by all of your skillshots. He will probably try and zone you out of the minion wave, but try and harass him as much as you can since he is melee. Be wary of where he ends up after using his gap closer, don't panic and immediately bind resulting in a miss. If getting chased by a Fizz, run erratically to lessen the chance of getting hit by his ult.
Galio can be a bit of a nuisance to a Lux player if he doesn't get shut down early. In the beginning levels, use your range advantage and harass him when he tries to last hit. Be careful and dodge his Q because it will chunk you for good damage. Later on he will try and push by clearing the wave with his Q+W combo, so use that opportunity to harass him while his abilities are on cooldown.
Karthus is a pretty easy matchup as Lux. Most Karthus players want to sit back and farm, your job as Lux should be to be as annoying as possible harassing them so they can't do just that. Karthus is also squishy early, so a couple E+Auto combos should be enough to make him back and give you the edge. If he walls behind you, instead of walking backwards and into it, turn towards him, snare and unleash your full combo. You should kill him before you take enough damage for his ult to finish you off.
Kassadin can be pretty rough for a Lux player, especially post 6. You need to do work on him early to push him behind in both farm and health. Poke with both autoattacks and your E any time you're not silenced. Once he hits 6, he will likely jump to you followed by an immediate silence. In order to win trades you need to have quick reactions in getting off your snare. One way to get around his harass is to push the lane because Kass is a notoriously bad farmer under tower.
Kennen is a champ that you should be able to poke easily considering that's what he's trying to do to you at the same time. The big difference is that you can stand behind your minions and negate all of his Q damage. If he rushes at you with his E, snare and back off. Always, always move erratically to avoid getting hit by Shurikens because they hurt a lot.
A good Leblanc player will destroy you as Lux. Rarely does this matchup go in the Lux's favor, and it's almost never fun. Pushing her is a good idea because Leblanc is bad at last hitting, but you need to be wary of how close you're getting to her. If she distorts towards you in order to Q+R, you'd better have your snare ready or you're about to be half health. Hold out as long as you can because Leblanc becomes less effective late game.
Thankfully, though Morg is one of the most common mid champions, she isn't hard to deal with at all as Lux. Your harass is vastly superior to hers, so constantly throw down Singularities at her feet and try and pop your passive as often as possible. Never ever run straight at her though (unless you are certain that her snare is on cooldown) or you could very much be dead. Try and be a nuisance as much as you can so that she can't afk farm by pooling the back lane creeps.
The difficulty of facing Orianna varies greatly depending on how savvy the enemy summoner is with her. A good Ori will be constantly moving herself and the ball, making it hard to harass her, and also being a nuisance hitting you as well. If she ever attempts to run and pick up the ball, snare her and blow your full combo. She should die unless she goes a tankier RoA build. Be unpredictable and do what you can to whittle her down.
Ryze is very weak early, so it's okay with you trade. One Q of his will not hurt as much as one of your Es, and if he steps forward to follow it up with a snare, pop your passive with an auto and snare him back followed by another auto. You should win these trades, and eventually wear him down so that at 6, he's dead. Learn towards the aggressive side early, a tanky late game Ryze can be a problem.
AP Sion is all about the push push push once he gets a couple Dorans Rings. You'll need to push back so he can't roam or your team will get ganked constantly. Stay out of stun range or you'll eat his combo and be hurting. An effective strategy is to bait him into committing by getting stunned, and then having your jungler gank him while he has no cc. Your snare combined with your jungler should easily take him out. Just be patient, Sion will fall off later if you can survive the early game.
Swain is played top often, but you see him mid sometimes as well. The longer tether length on his slow is pretty killer, so try not move the same direction every time you get slowed or you will eat one of his snares. You're going to need to use ignite every duel or he will not fall to your burst because of his sustain. I also highly advise warding his blue and trying to steal it when possible.
Talon mid is something you may see if you end up picking Lux pretty early in the draft. To be honest it's pretty rough. If you're IP rich, invest in an AP mid page that has armor yellows, they help a lot. You might also consider going for an early catalyst into a Rod of Ages in order to not get blown up by a Talon. Play passive and farm when you can, later on you should be able to survive his burst and you'll be more useful with your utility in a teamfight.
Laning against TF will take a lot of movement in order to dodge his Wild Cards. Standing away from your minion wave will help combat this a lot, so try that if you find yourself getting hit too often. When TF uses his Pick a Card on a minion ATTACK! When that spell is on cooldown, he is very vulnerable. Plus, it's hard for a TF to pick the right card under pressure sometimes, even pro players can blunder at that. If you see him leave lane, try and guess where he went and follow. Obviously his Gate is faster than you walking, but most times you should get there in time to help and hopefully turn the gank around.
Playing against a Veigar is pretty precarious at times. His range is pretty short, so you should be able to harass him effectively early. If he tries to harass back, he will get behind in his Q farm, and his mana pool will deplete quickly. If you get stunned, pray to high heaven though because a combo from Veigar will hurt bad. Keep your distance and poke away until you can finish him with an ult.
I find Viktor to be hit or miss a lot, kind of like Orianna. In the right hands he can be a pretty big annoyance mid. The range on his laser is pretty far, but if you stay out of your own minion wave, he will have to pick between harassing and farming. In the event that he tries to run up to you to Q, snare him and follow with a combo. If you do ever get ulted, throw down your shield as soon as you can in order to soften the DoT.
Vlad is seen top more often than mid, but he can perform both pretty well. His sustain is ridiculous mid game, so try and make the lane hell for him early. If he walks forward to Q you, make him pay with a Binding+Auto+E+Auto combo. Punish him every time he tries to trade. If you can, force him to pool and then either get a gank or attack again soon after. If you get ulted, be sure to shield yourself before the second tick.
Xerath and Lux are both high range burst casters, so this is always a fun and competitive lane. Again, standing outside your own minion wave will make Xerath have to choose between harassing you with Qs, and using them to farm. If you ever see him lock down in range of your snare, hit him! Don't be easy to read when walking around or you will eat a ton of his Qs.
Zyra has decent range and nice damage to complement her kit. Poke her as much as you can, and be sure to run erratically to avoid her snare. Trying to pop your passive can be difficult against a smart Zyra. If you're getting DPSd down by her plants, remember to shield yourself and never forget about her passive.