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There are a number of reasons why a lime tree might not bear fruit. Here is an article that you may find helpful: https://www.gardeningknowhow.com/edible/fruits/lime/reasons-and-fixes-for-lime-tree-not-producing-blossoms-or-fruit.htm

If you have never had a lime tree, it can be hard to tell. This article will help you: https://www.gardeningknowhow.com/edible/fruits/lime/lime-tree-harvest-time-when-to-pick-a-lime-from-a-tree.htm

Try neem oil on your plants. It is effective against many types of insect pests but perfectly safe for you, your pets, and beneficial insects. It is also an effective fungicide. Here is more information: https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

I would also try giving it some phosphorus rich fertilizer, like bone meal. If it is lacking phosphorus, it will not be able to produce blossoms. If you have not read it yet, this article may also be helpful:
https://www.gardeningknowhow.com/edible/fruits/lime/reasons-and-fixes-for-lime-tree-not-producing-blossoms-or-fruit.htm

Typically, leaf loss is due to irregular watering, where the tree was without water for a period and then, when watered again, will drop leaves. Here is an article with more information: https://www.gardeningknowhow.com/edible/fruits/lime/lime-tree-leaf-drop-why-a-lime-tree-is-losing-leaves.htm Lime trees usually require a nitrogen-rich fertilizer, with more phosphorus early on (prior to blooming). Here is an article that you may find helpful: https://www.gardeningknowhow.com/edible/fruits/citrus/fertilizing-citrus-trees-best-practices-for-citrus-fertilizing.htm

Here is an article that you may find helpful: https://www.gardeningknowhow.com/edible/fruits/lime/is-lime-fruit-and-lime-blossoms-falling-off-tree-normal.htm