Jared has given a good answer. The word "on" can indicate that something is continuing, so you might see various phrases like "walk on" (keep walking) or "go on" (keep going). And as Jared says, the word "on" in the first sentence describes the light. The word "in" is part of the description "in every room." (You could reverse the sentence structure and say, "In every room, the lights were on." The meaning is the same.) The words "on in" don't make sense together as a phrase, but you will sometimes see them together in sentences where the word "on" goes with a different word earlier in the sentence.

There are two sentences like : 1.The lights were on in every room. 2.We walked on in the forest, one behind the other. what situations do we make sentence using "on in" together? Thank you ! In the first sentence “on” is being used in the sense that the lights are functioning. In the second sentence, on is essentially shorthand for onward, meaning “continuing forward.” The second sentence should look like this: “We walked on into the forest, one behind the other.” or “We walked onward into the forest, one behind the other.” The sentence using onward would be more correct, but the one using on would also be understood just fine.