It seems that the Romans would dry clean their laundry with ammonia derived from urine. Considering the source of the ammonia, and the smell of pure ammonia, I find it hard to believe that this connection was ever made. How did one come to the conclusion that soaking clothes in a stinky fluid derived from urine would make it cleaner?
Urine was also widely used for improvement of leather. It was quite natural to try and put in it something else. Hmm... But I wouldn't call it "dry clean" :-)
Ancient cultures had so few chemical reagents to try, that they tried everything on everything. For example, they hardened steel in urine, too. Tried multiple materials to see what urine is the best for - old, new, that of a goat or of a man? What man? young or old? And so on.