Q.I Have a Lime Tree That Won’t Produce
The tree is four years old and eleven feet tall.

Certified GKH Gardening Expert
Have you fertilized? Nitrogen encourages leaves to grow, but not fruit. Too much can actually keep a plant from producing fruit. This article has information on how to fertilize your trees: https://www.gardeningknowhow.com/edible/fruits/citrus/fertilizing-citrus-trees-best-practices-for-citrus-fertilizing.htm
Sometimes when fruit trees produce little to no fruit, the soil may be lacking phosphorus. Add bone meal and have your soil tested. This article will explain more: https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/phosphorus-plant-growth.htm
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