both critters are extremely resilient, I don't believe either will drown.
If they did they wouldn't live so long, lice for instance remain on humans throughout baths & shampooing.
Buy a good flea bath shampoo for dogs and give them a nice long soaking scrub with plenty of the stuff, that will help to stun & kill most of them.
Then powder or spray the entire coop & saturate any wood with spray from your local place.. pyrethrin or permethrin should work. Recommended around here is Adam's Flea & Tick Spray or Sevin dust or the Adam's powder equivalant. Repeat in 10 days
Then after your chooks are dry & fluffy, dust their bodies including under the wings at least every 10 days until your certain they are all gone.
I have found that Selamectin (Revolution for dogs & cats) works fantastically well for mites, but not the lice.
After that keep a dusting area for the chooks with a bunch of the powder so they can maintain themselves. Once the infestation is taken care of, dusting every month or so, and keeping some in the dusting spot should keep everything at bay.
Honestly, the only non chemical way I know of to get rid of any of the mention bugs is a fire.
It's WAR... you MUST win!