We have a tree with leaves that have a strong lime smell but the tree doesn’t bear fruit. We were wondering what the name of it is

Question

and does it like direct sunlight.

Answer 1

I don't find anything that smells like limes other than limes or wild lime. My next thought is you need information on how to get it to fruit:

https://www.gardeningknowhow.com/edible/fruits/lime/reasons-and-fixes-for-lime-tree-not-producing-blossoms-or-fruit.htm