This is the way to go if you want to eliminate rather than just manage the infestation. I've had good luck with Bonide Tree and Shrub but just be sure to follow the provided instructions for ornamental plants.
I get wicked aphids in my trees. I use a few of these on my big guy 30 inch oak to kill the aphids and it does a great job on lantern flies as well.
Bonide (BND611) - Annual Tree and Shrub Insect Control, Insecticide/Pesticide Concentrate (1 gal.) https://www.amazon.com/dp/B002ITL19A/ref=cm_sw_r_apan_i_6JM2YW0P6MA5VAE6907E?_encoding=UTF8&psc=1
Bonide annual tree & shrub systemic insecticide be used as a soil drench for houseplants.