Let's get rid of "many" and see what happens.
Everything was lit with a dim, crimson light; the curtains at the windows were all closed, and the lamps were draped with dark red scarves.
This wouldn't make any sense without "the", since it wouldn't specify which lamps were being talked about. With "the", it's clear: all the lamps in the room.
Now we want to add that there are a lot of lamps in the room. We are trying to say that the lamps have the property of being "many", so we use "many" as an adjective. If we still keep the word "the", we're still talking about all the lamps in the room.
Now we could drop the word "the", and the sentence would still make sense, however it would have a slightly different meaning.
Everything was lit with a dim, crimson light; the curtains at the windows were all closed, and many lamps were draped with dark red scarves.
This version says that there were a lot of lamps draped with scarves. But it's no longer clear that we're talking about all the lamps in the room. There could be some other lamps that weren't draped with dark red scarves, and in fact this wording suggests that there were (just as saying "many people like Harry Potter" suggests that some people don't).