Q.kill mites without harming green lacewing
I have severe mite problems, and green lacewings are not keeping up with them. I would like to use something in addition to the green lacewings that won’t hurt them.

Certified GKH Gardening Expert
Avoid using any insecticides, and look for a miticide (acaricide) that is not also an insecticide:
https://www.gardeningknowhow.com/plant-problems/pests/pesticides/using-miticide-on-plants.htm
http://ipm.ucanr.edu/PMG/PESTNOTES/pn7405.html
https://entomology.ca.uky.edu/ef438
https://www.gardeningknowhow.com/plant-problems/pests/insects/common-mites-affecting-plants.htm