Never lubricate a dirty chain on the bike. I remove my chains, clean them in Simple green and water with an ultrasonic cleaner. Rinse, dry remount and lube the chain with 4 parts mineral spirits to one part chain saw bar oil. I repeat every 750 miles.
I wash the bike with Dawn dishsoap. I don't like Simplegreen on the tires. If you use Pledge on the bike after you clean it it will look good and cleanup easier the next time.