Yes, I've attempted to induce a lucid dream before, and was successful in doing so. However, it does take practice to be able to fully control it.
Also, sleep paralysis actually is more likely to happen to those who have a mental illness than those who don't. It can happen to anyone, mind you, but those with depression or anxiety and such are more susceptible to it. And yes, lying on your back also makes it more likely to happen. So does lucid dreaming, actually. A lot of people have experienced sleep paralysis when waking up from a lucid dream, myself included. Nevertheless, it's still worth it, in my opinion, to practice lucid dreaming.
By the way, to wake yourself from sleep paralysis, people say that if you try to move a finger or toe, it can help to wake you. Although, my personal way to wake myself is forcefully try to shake my head until it wakes me up.