Kaffir Lime Plant
My plant has gone all sticky and looks like lots of sticky strands. It also looks like it may have an infestation.
Certified GKH Gardening Expert
There are a few pests that can cause this, such as aphids or scale. Fortunately, they can all be treated with a general pesticide.
I will say though, these pests tend to attack trees that are stressed. You may want to check and see if there is anything that may be stressing the tree, such as a lack of nutrients or improper watering.