I have a lime tree in a pot that seems to be quite healthy, yet it is only showing 1 lime the size of a ping pong ball and 5 more very tiny ones (all are on the same branch of the tree). It's been growing for about 5 months now. It had no fruit when we bought it.
Lime Tree Lack of Fruit
Certified GKH Gardening Expert
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, https://www.gardeningknowhow.com/edible/fruits/lime/reasons-and-fixes-for-lime-tree-not-producing-blossoms-or-fruit.htm