Why do I get sleep paralysis in my dreams sometimes?

So a couple days ago I had a dream I was in the kitchen with my family I was standing by the sink. For the second time ever lucidity was achieved by random unconscious thoughts within dreams. I was staring at the silver sink when a thought crossed my mind (details in dreams are hard to remember but so the thought I had might not exactly been what I'm about to say it was) the thought was something like "well this would be fun to do later although.. I'm dreaming." If that was exactly what I thought then that must of been my unconscious mind bringing up the point there is no saving this for later because later it won't exist. Anyways after that thought went through my mind I realized I was dreaming the lucidity was short lived however I almost immediately woke up into sleep paralysis, or I thought I woke up into sleep paralysis I actually had a false awakening into sleep paralysis. I did not realize I was dreaming mainly because I know sleep paralysis happens when your still somewhat conscious so the scenery would be real. When I had the false awakening I was able to move at first but my body locked up while I was laying on my stomach. I tried to move had some success but very little, couple seconds later this man came in through my door and began aimlessly speed walking around my room without any apparent reason or goal, and the strange randomness of it shot a shiver down my spine but I knew it wasn't real so I wasn't scared just creeped out. The false awakening sleep paralysis end followed shortly after I was able to watch the tv my real ears were able to pick up the sound and voices coming from the tv (it was a morning cartoon on Cartoon Network) the characters I saw in the dream were normal but were doing things to random for it to be real but didn't pick up on that to I woke up. When I woke up I looked at the tv and I did notice what was on the tv didn't really add up to what it was in the dream which is when I proved to myself the sleep paralysis was in a false awakening not reality. Just wondering if it's common for people dream of having sleep paralysis and maybe especially after a lucid dream since I know false awakenings are common after lucid dream.