I don't artificially light my chickens but I get a drop in eggs when ever the weather either changes a lot suddenly (hot, cold, hot, cold- or hot, rainy, hot, stormy) or when it is hot (over 90*f) for along time many days in a row).
I doubt a light will help really, age slows them down.
I'd check again to make sure that they are not eating them, can you tell us what there diet is.
I don't leave lights on for my birds so mine do natural chicken things (moult, take breaks), my customers prefer eggs as natural as possible...