Your peacelily was just happy to have some loving as well as after the major shock of infestation.
The soapy water works as mealy bugs have their fluffy white waxy coating. Key word obviously being wax and we all know that dish soap is made to "cut through the toughest of grease".
Another thing that works and doesn't harm plants (depending upon which brand you purchase) is diluted tobacco...let me explain why and how.
Why:
Mealy bugs are like ticks for plants and they suck the sap from them. Watering your plants with a tobacco tea kills the bugs because they end up 'drinking' tobacco.
How:
Purchase a pack of unfiltered preferably natural-esque cigarettes...think Lucky Brand or Native Brand. Do please avoid flavored tobaccos and anything that maybe too overly chemically processed. And I say no filters because those just go straight to the landfill and last for decades. But I digress. Unwrap the tobacco and let sit in water overnight - effectively making a 'tobacco tea'. Then sparingly water your plants with diluted tea over a series of weeks - you do not want to shock your plants with this method just devoid it of creepy crawlies. Also I say over a series of weeks because you want to get the adults, larvae and soon to be hatched eggs on your poor plant.
This was a home remedy that my teacher in high school used in the green houses, it will also work for any other sap sucking type insect. Just do not get it on your skin
