Without video it's hard to say what you did wrong.
Skillshots are really about mindgames. You're trying to anticipate where your target is going to be, and tossing your skillshot to hit them at that future location, while they're trying to confuse you and juke the skillshots.
I assume you know that basic, and how in a gank to use skill shots to coral a target so that if they do juke your bind, they're moving in a direction that puts them away for their turret / team / safety, and in a place they're more vulnerable.
With Lux, especially at lower elo's, remember your bind hits two targets. Most people just stay behind minions to dodge skillshots, and you can abuse that habit with your bind, hitting a minion and then your enemy with the second binding.
Using your e slow to help your q also works rather well, though if people are easily dodging your e, it sounds like you aren't positioning it optimally and giving them easy avenues of escape.
Since skillshots are mind games, the best time to land them is when your opponent doesn't expect it. Like using a skillshot when they move in to last hit. Early on a kayle can't keep her e up constantly, so you have opportunities where you know exactly where she's going to be positioned and can punish her for it. It's also good to realize that you don't necessarily have to spam your abilities punishing them. Sometimes scaring them enough that they zone themselves from cs is better than being oom and having them shove to your tower. For champions like lux, getting jungle assistance early can really make that fear factor apply better.
Beyond the above it's really just practice that makes you better at skillshots.
I'm far from an expert, having only reached as high as silver 3, but at least at my level of skill the above seems to work well, though maybe a diamond or plat will tell you to completely disregard what i've said. I dunno. O_o;
