Depending on your opponent there are different items which help you to defeat them.
Against heavy AP getting an abyssal scepter increases your durability against AP and increased damage
Against heavy AD or AD mid Zonya's hour glass gives a nice amount of armour and a 2.5 second invisibility which may save your life and can be used to avoid incoming ultimates like ziggs or zyra.

Your Q can hit 2 targets, use this to your advantage to enemies hiding behind there minions

Your W sends out a shield, shielding all allied champions it passes through. Moving lux once the shield has been thrown out will control the direction and return of the shield.

Your E throws out an AoE circle on the ground which slows all enemies that move across it. After 5 seconds the circle will detonate dealing damage to all enemies walking over the circle.

Your R fires a long range laser dealing high damage to all enimies it hits

Lux excels at controlling her lane, use her abilities to control your opponents position for ally ganks.
Try to deny farm by constantly harrasing with your E
Also use your E to get minions low, your passive will make it extremely easy to last hit after.
Do not use your Q for last hitting (wasting mana), your E applies your passive to multiple enemies not just 2.
If your playing an aggressive lane like leblanc it may be worth upgrading your shield twice before you reach level 6

Against skill shot reliant champs like Lux, Morgana, ziggs, xerath, diana ect... buy your boots and only 1 dorans ring to avoid there combos.

Countering
Ahri- Poke her down. Early boots (avoid charm and orb). Her dash makes her tricky to chase, but landing your Q should let you get enough damage(not for a kill)
Anivia-Very squishy champ, early game poke will be effective. When she dies use your E on the egg and use all CD's besides ult to destroy it.
Annie- Check her buffs to see if she has 4 stacks, if she does try not to engage and keep poking her from a far.
Brand- Early boots should be enough to dodge. When he uses his ult seperate yourself from an nearby allies or it will remain bouncing between you all dealing more damage than it should.
Casseopia- Early boots. Focus on avoiding her poisons or she will burst you.
Cho'gath- Again early boots and just poke him down. Dont let him consume you!
Dianna- Hard to defeat after she reaches level 6, use your shield if she gets her moonlight de-buff on you.
Elise- Try to avoid her exploding spiders. If your low health it may be worth using your Q to stop the spiders. Try to deprive farm and an early kill helps.
Fiddlesticks- Any small poke will be useless short term as he will just drain health back. He is heavily mana reliant so try and waste his mana quickly. It is important to report missing lane his ulti is OP
Galio- Keep harrasing him and focus on farm.
Hiemerdigner- Kill them turrets and beat the **** out of his tiny yellow ***!
Karthus- Stay at a long range and only get close for last hits. Using your shield when you see his ult coming down on you will protect you from most if not all the damage. Use your snare to stop him getting close with his AOE
Kassadin- Take advantage melee auto attacks by depriving him farm as much as possible. Try getting an early kill before he gets his ultimate.
Kennen- Try staying behind your caster minions to avoid his skill shot. Snare him if he turns into the electric orb
LeBlanc- Make her move around allot by harrasing with your E, make er miss as much farm as possible.
Lux- Shoot through there minions and get farm. Use your shield if she engages, most luxs dont use it properly
Malzahar- Harass him constantly not forgetting about farm, once he has used his ult go in for the kills
Morgana-Use your Qs ability to pass through 1 minion to start attacking morgana before she can start on you.
Orianna- Dodge them swinging balls
Ryze- Getting MR helps allot ( get abyssal scepter early on ). If you get caged make sure to throw your shield out.
Swain- Get morellos (upgrade to chalice) instead of your athenes for the heal reduction.
Syndra- Early boots, stay at a long range and keep sniping her down.
Talon- Deprive him from farming and stay behind your minions, incase he jumps to you.
Vieger-Building an abyssal scepter is important, or he will just burst you down. It is difficult to catch without hard CC but even with event horizan and flash he will most likely get away.
Viktor- try farming from a distance and avoid (if possible) his laser, getting early boots helps and through out your shield before you get stunned by his ult
Vladamir- Dont him unless he is low, he will just turn into the period puddle. Ask for an early gank to waste his flash and some health if not a kill.
Xerath- There is a long delay on his attacks so cast your shield out if you see one coming at you.
Ziggs- Early boots and dont let him farm.
Zilean- Throw out a shield if you see a bomb on/near you.
Zyra- Dont stand on plants. If you see the ult circle throw out your shield

Take advantage of luxs great range by positioning yourself at a safe distance during team fights.
Focus on snaring escaping enemies during the end of team fights.
Using your ult before you get to / during team fights is good, the cooldown is so short it will refresh by the time you need it, unles you want to be a ks little *****.

Keep shielding you allies to block/reduce any incoming damage.
Keep snaring for damage and reducing mobility to enemies making ganks easier.
You can use your E to slow chasing enemies, depending on the chasing enemy and there range you can use Q W and E to help your ally. When being chased by enemies with dashes/flashes and long ranged skill shots like Akali or Xerath its best to shield your ally first then throw an E onto there path.
With very fast champions throwing your E down first will be more effective, when inside the circle try and land a Q.
If the enemy is running directly at you and has no flashes/dashes then go for a straight Q and place an E behind you.
Note: this also applies if enemies are chasing you.

The standard skill sequence for lux is
W (before entering combat) -> Q -> E
Try landing an auto attack before you explode your E to get an increased duration form your passive.
Depending on the targets health you can fire your Ult while the target is snared for a garenteed hit and high burst damage. I never usualy cast my ult unless i know its a garenteed kill or will help your allies.