I never had a problem with Lux's Q usually. Sometimes stuff happens but sometimes that can just be equated to a latency problem (all spell effects when a lag hitch happens have similar symptoms).
I have had too many issues to count with her laser though. Sometimes I shoot someone and they're in the middle of it and it just does no damage. Similarly, I've been stuck in to the side of a Lux laser (not in the middle, but still clearly in it) before and... nothing. No damage. Still alive. This is more apparent at the end of the laser, especially when firing up north due to the camera angle.
Alternatively, I've been and seen other people be well clear to the side of the laser and still get nuked as well. It's like the width of the hurt box changes every time.