These examples are a minefield, because lay and lie have the most confusing similar meanings and even overlapping past tense forms. Many people do not use them in the standard ("correct") way, and don't even know the right way. You don't always use the same verb between lay and lie in your examples, and you don't always use the right one in the right place, so I will try to explain those as well.
Technically speaking, the correct way to form the first sentence is:
When she walked in, he was lying on the bed.
The grammarian standard rule is that lie is used when the actor or subject of the sentence is the one who is lying down (which is what is happening in your sentence).
Now, with this correction in mind, on to the answer: technically all of your sentences are correct, but they all mean a different thing.
You use the past progressive when you want to describe an event in the past that took place during another event in the past. So, in your first sentence, "she walked in" is one event that happened, and "he was lying on the bed" means that the walking-in happened during the lying.
In your second sentence, you are have two simple past tense verbs. This time, "was laid" is a passive construction in the past tense (past tense of "lay", specifically). Since the sentence is passive, it means that someone laid "him" on the bed — he didn't do it himself — so the past tense of lay (rather than the past tense of lie) is the correct verb to use. So, this sentence means that at the moment she walked in, someone or something laid him on the bed.
In your third sentence, you again have two past tense verbs. The verb lay is the simple past form of lie, so you are saying that the walking-in and the lying happened at the same moment in the past.