i lie down in my bed is correct

We use ‘lie in bed’ when we are talking about someone who is already in bed, e.g. She lies in her bed, reading a book. ‘ Lie down’ is a phrasal verb that signifies the act of getting into a flat position, ready for sleep. For example ‘I’m tired so I’m going to lie down now.’ Hope that’s useful, Helen

"lie down in my bed" and "lie in my bed" have slightly different meanings. The first phrase means that I have gone to my bed because I want to sleep. The second phrase means I am already in my bed; maybe I've been lying in my bed for an hour, and I really want to sleep! I hope that helps. :-)