Shenaii wrote:

I don't normally remember my dreams, not even as soon as I wake up. I'm not too sure if I am dreaming at all, but if I am, would Lucid dreaming let me remember my dreams?

Yes, since the purpose of lucid dreaming is being aware while dreaming.
One tip you should try is instead of abruptly waking up, take like 2-5 minutes wondering what the hell you dreamed earlier. Your dream data in your mind expires pretty fast so the sooner you wanna get your hand on it, the more chances you'll have recalling the dream. Another really effective tip is meditation (worked for me). Also, right after physical effort your mind is actually sharper so may try that if you wish.

Thanks, I will certainly try the tips

As Revo mentioned,dreams tend to forget fast.The first thing you need is to write a dream journal after you wake up.