The lamp left on is a small message that arrival is still expected.

A light in a window does a job that words would make awkward. It says someone is expected without anyone having to wait up or make a fuss, and it says it to a person who may be tired and not in the mood to be met at the door. Small signals like this carry a lot because they cost the giver almost nothing and reach the receiver exactly when they need them.

Think of who is coming home to your house, or your message. Leave the equivalent of a light on: a made bed, a short note, food in the fridge, something that says you were thought about.