Red Bug On Persian Lime Tree

Question

have used neem oil, but never seen this bug before
Have black residue on some leaves and limes
don’t know if it’s related

Answer 1

It sounds like you may have spider mites, or "citrus mites." Make sure the area around your tree is clean and free of debris. You can use an insecticidal soap on these pests, which you can either make up at home or purchase from a garden center, but I suggest you do it right away.

These articles will help:
https://www.gardeningknowhow.com/edible/fruits/citrus/citrus-mite-problems.htm.
https://www.gardeningknowhow.com/plant-problems/pests/insects/red-spider-mites.htm
https://www.gardeningknowhow.com/plant-problems/pests/pesticides/homemade-soap-spray.htm