Q.Why Has My Lemon Tree Got Sticky Leaves?
This is so bad it’s dripping onto the floor

Certified GKH Gardening Expert
This can be caused by infestation of many insects. Typically, this will be spider mites, scale, or aphids. Aphids are easily spotted. Scale is easy to spot if you know what to look for. Usually, you will see soft scale. They are flat and brown, and they can be mistake for part of the stem. They will flake off, easily when you rub the stems and bottom of leaves. There is the more notable hard scale, as well, but those are easy to spot. The worst one, however, would be spider mites. They are difficult to get rid of, and they can be hard to see. Persistent treatment will be the only way to get rid of these. These articles will go into detail:
https://www.gardeningknowhow.com/plant-problems/pests/insects/homemade-aphid-control.htm
https://www.gardeningknowhow.com/plant-problems/pests/insects/what-is-soft-scale.htm
https://www.gardeningknowhow.com/plant-problems/pests/insects/control-plant-scale.htm
https://www.gardeningknowhow.com/plant-problems/pests/insects/spider-mite-treatment.htm
https://www.gardeningknowhow.com/edible/fruits/lemons/how-to-grow-a-lemon-tree.htm
These articles will help: