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He lives / is living in London now. (Which one is correct)
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Both are fine. The second shows increased interest, concern or immediacy on the part of the speaker.
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Maybe some examples will help you understand when you might use one over the other.

You meet someone for the first time, and begin talking about your families. He says his sister lives in Rome. You say your brother lives in London. "He lives in London."

You meet an old friend, who is aware that your brother has lived all over the world as a journalist. He asks about "Bob," and you say, "He is living in London." In this case, I think you would choose "is living" for the immediacy that MM refers to above. If someone is just living there for now, and has lived or might live other places, "is living" is more commonly used to denote that.

If they are pretty permanent or there is no reason to convey immediacy, or increased interest or concern, you would probably choose, "He lives..."

How to use modal auxiliaries in future form? Especially about Shall and Will. I have confusion about these.

He is living in the usa

Students: We have free audio pronunciation exercises.

They're living in a motel while their house is being remodeled.

Not They live in a motel while ... (unless you're referring to the unlikely case where they have their house remodeled on a regular basis).

CJ

He is living in

London now