I think you can Ana but you can't lay down on your back. You have to lay something down. It can be yourself or an object. But you can only lay eggs or tables. Your choice
Glad you brought this up mrsmopp - I too find it very annoying. Another current usage that sets my teeth on edge is 'floor' for 'ground' i.e. 'I tripped on the pavement and was laid on the floor' - No!, No!, No! [shudder]
I think it is actually lay the table and I am lying in bed. I know I wrote late last night on the iPad section that I was laying in bed, but I am not a fork I am a person, so I should have written I am lying in bed.
So glad you liked it Elegran, I can't remember where I heard or read it but it has helped me to remember the use of the verb. I will have that lovely mental picture to add to it now as well!
mrsmopp Two different verbs, the verb to lay (hens) and the verb to lie (people) Hens lay eggs. People lie down. (Present tense) The hen laid some eggs. The people lay down on the beds. (Past tense) The hens were laying some eggs. The people were lying on the beds (past imperfect) Sorry, but you did put it in pedants' corner and I have no doubt that someone, probably absent, will be along very shortly to correct me