I know that 'I'm in bed.' is correct. I also know that 'lie down' is (also) a transfer verb, in that one assumes the horizontal position in bed either when already being in bed, or coming from out of bed.
So please tell me whether I'm right when saying that each of the following is correct for its own meaning:
'Lie down in bed' = assume the horizontal position when already being in bed.
'Lie down into bed' = assume the horizontal position in bed, coming from out of bed.
Many thanks.