Q.lime tree dying
Lime tree was really productive and now appears to be dying, so what can I do? Half the tree still has some fruit but other half is practically dry and twigs can be snapped off.
Leaf and twig die back are generally due to plant stress or disease.
Verify the watering and fertilizer schedule.
I'm listing several links to help you closer pinpoint the issues.
https://www.gardeningknowhow.com/edible/fruits/lime/lime-tree-tips-care-of-lime-trees.htm
You should inspect the tree carefully to look for signs of pests or disease on the leaves, fruit or trunk of the tree.
https://www.gardeningknowhow.com/edible/fruits/lime/problems-lime-trees.htm
https://www.gardeningknowhow.com/edible/fruits/lime/lime-tree-tips-care-of-lime-trees.htm
https://www.gardeningknowhow.com/edible/fruits/citrus/greasy-spot-fungus.htm