You'll need to spray them with an effective insecticide if you want to save this tree.
I wouldn't waste time with vinegar, Dawn dish soap, or any other home-remedy. They won't work.
Insecticides with the active ingredients dinotefuran, imidacloprid, carbaryl, and bifenthrin are effective at controlling the spotted lanternfly.
Bifenthrin or Carbaryl are what you'll need to kill these adults.
As a homeowner who has despaired at watching trees die, I have become comfortable with buying concentrates, mixing them, and spraying my trees and greenery to effectively kill invasive pests. It works.
Just be sure to work safely with any commercial pesticides. Wear a respirator, gloves, and do NOT mix them indoors (especially the kitchen) where accidental poisoning can occur. Keep kids and pets indoors while spraying, and avoid spraying non-infested areas, to limit the harm to beneficial pollinators.
A cheap garden sprayer and Bifen at 2 oz per gallon. Maybe 3 times a year.
Bifen IT 128oz- Bifenthrin Insecticide Same as Talstar Pro https://www.amazon.com/dp/B00GLEO6EA/ref=cm_sw_r_cp_api_i_8KGH6EE8DAR5A88JY96Z?_encoding=UTF8&psc=1
you will have no mosquito problem