For the first two, to lie (or to lay) is being used as a linking verb. Linking verbs can take adjectives as complements in place of a noun or noun phrase as objects. Lie and lay are not always linking verbs, but they are sometimes.
The simple (but not flawless) way to tell if a verb (that doesn't have any auxiliary verbs currently attached) is being a linking verb is if it could be replaced with the relevant for of to be and still make sense. If there are auxiliary verbs, it's more complex.
So, looking at your second example, we can turn it into:
He is motionless under white sheets in a bedroom
The first has an auxiliary to be attached to it already, so we have to work out what the equivalent to be form will be. Taking it as a literal conversion we get was being, and that gives us something that makes sense - is just not how anyone would say it:
I was being half-asleep on my sofa
Let's call that:
I was half-asleep on my sofa
Now, in both cases we've lost meaning, but we haven't become completely meaningless. Verbs that are more often linking verbs include to appear, to seem, and to look, but many have non-linking senses as well.
Linking verbs are those that refer to appearance, status, having characteristics, and so on. They do not describe direct action or control by the subject. Now, there's direct action when you lie down, but if you're just lying, you just lie there. So we have a subject, a linking verb, an adjective, and an adverbial of place.
The other two examples are a little more complex. I would say they were set phrases which most likely started as having adverbials that suffered from ellipsis to get rid of extraneous verbiage.
They burned the ants while they were alive
Bring him back while he is alive
But that's a hypothetical. What we can say is that there is a pattern that allows us to put an adjective describing the object after the key components of the S-V-O, even if words have been shifted in their order. Whatever the cause or development, what we can do describe the object with an adjective at the end of the phrase, at least in some cases. Sometimes it describes the state of the object at the start of the action, and sometimes at the end.
I'll beat you bloody
Though that could be ellipsis again
I'll beat you until you are bloody
There are different ways to explain it, and I expect you'll find linguists have come up with more explanations than I have. The easiest is probably just to consider "bring X back alive", "beat X bloody", and "burn X alive" as set phrases - among many others.