Yes, she is rather weak at the begining of the game. She's a carry. But if you buy Mejai's Soulstealer as soon as you can, get some kills or assists in and don't die, you will dominate. Soulstealer + Archangels Staff + Deathfiregrasp = dominance.
Use CD reduction runes and spec 9-0-21, you will be able to fire off your ult about every 15 sec that will do around 900+ dmg. Most champs will have around 2k health at late game. In other words, you're able to knock off half their health every 15 sec. Not only that, but you'll be able to use your snare and your slow every few sec that will also do a decent amount of damage.
All in all, people who want to play as Lux need a lot of practice with her. She is one of the most difficult champions to play, but can be one of the most powerful if you know how to play her.
A Buyer's Guide to League of Legends: Lux
While Lux is definitely one of the most fun champions to come to the League of Legends, can she really contribute at the higher levels?
This brings me to my second problem with Lux: the general underwhelming power of her spells. While Lux's 'Q' spell, "Light Binding," deals decent enough damage in the early game, it scales badly at +0.7 damage per ability power. Not only that, but because Light Binding is a snare and not a stun, if a good Lux player catches a ranged enemy in her snare, she can't afford to hit them once to pop Illumination for extra damage. Since enemy champions can attack while being snared, they will often hit Lux as she tries to attack them; given Lux's extremely fragile defensive stat growth, this can sometimes translate to a bad trade for Lux! 
Lux's shield has the potential to be just as powerful as Morgana's "Black Shield" in a team fight because she can potentially shield all of her teammates, but this never works in practice. Part of Morgana's great utility lies in the incredible scaling potential of her Black Shield (+0.8 per ability power) combined with the fact that Morgana's shield negates negative statuses. This is simply incredible against magically weaker champions who utilize a lot of disables (Lux does come to mind here). Morgana's shield is also instant, so you get a lot of those great moments where a killing spell is in mid-flight, but Morgana utilizes her shield perfectly to block the damage. For Lux, since her shield is a straight-line skillshot that isn't instant, she is typically reduced to throwing her shield out onto her entire team, hoping that it will help them in the long run (given her shield's low, low scaling of +0.3 per ability power, this is rarely the case).
Finally, while Lux's Lucent Singularity is an interesting spell for its mobility hindering purposes, because it deals no damage before its 'popped' - and it deals very low damage when it is popped! - enemy champions have learned to simply walk through the slow without hesitation. Other champions with similar spells, like Anivia's Glacial Storm ultimate, Morgana's Tainted Soil or Nasus' Spirit Fire are used to intimidate enemy champions; they instantly make the enemy team want to get off the spell, and this intimidation is what makes these spells so effective. Unfortunately, there is nothing really intimidating about Lux's Lucent Singularity - while the slow is annoying, there is no real punishment (aside from taking low damage) for staying in her spell, and this can be frustrating for Lux players.
In the end, while I cannot stress how much fun Lux is as a champion, if you are looking for a strong supporting character to use at higher levels of play, then Lux is not where you should begin your search. Until Riot decides to give her some significant buffs to let her contribute more to her team, stay with champions who bring more utility and damage (Zilean, Sona and Morgana all come to mind). If, however, you just want to enjoy running around firing lasers, well… by all means!