Update:No, it is not a fig tree or a lime tree. It is a walnut tree. The light brown shell of the walnut that we are all familiar with is covered by a green peel.
In the Song of Songs (6:11) it is written:
"I went down into the garden of nuts, to look at the green plants of the valley, to see whether the vine budded, and the pomegranates were in flower."Why do you have to go "down" the the garden of nuts? One possible answer is here.