lie down/in

1a. Lie down.
1b. Lie in.
2a. Lie down on the floor.
2b. Lie in on the floor.
Please correct the above.
Does 1a mean 1b and also 2a mean 2b?

2b is incorrect.
‘Lie in’ either means to literally lie inside something:
I could lie in the bath for hours.
or it means to deliberately stay in bed later than usual in the morning:
I had a lie in this morning because I didn’t have any appointments until after 1 p.m.

‘Lie in’ is also used while referring to the ‘lying-in’ period of women (after/around delivery).
(This is common among South Asian people)

OK. It wouldn’t be used in Western ciivilisations.

Why mention civilizations? The Oriental one attaches greater importance to its women.

Oxford dictionary refers to maternity hospitals as lying-in hospitals, indicating/implying the use of lie in with that meaning.

I mention it because some people might like to be aware of that fact.
The term may have been used in the 18th Century, but that was some time ago now!