Limes must be planted to grow lime trees. They cannot be found naturally.
Lime trees have brown/gray trunks and green leaves. Some trunk blocks will have leaves overlaying them, but they are still part of the trunk. There may be limes hanging upon the leaves.
Lime trees occasionally will spawn limes from its leaves. Limes, if in season, are harvested by hand and can be collected by passing through their space or when adjacent to the lime after it was tapped on. They do not require nor do they benefit from using any particular ツールs|tools. Agriculturally, the fruit can be placed in a block of dirt or compost to grow an lime tree for farming additional limes or can be eaten to replenish a Blockhead's health and hunger bars.
Wood may be also harvested from the tree's trunk. Doing so will despawn any leaves or trunk blocks on the same layer or above. For harvesting wood, using an axe will produce quicker results and a larger yield than by hand.
Lime trees die similarly to other trees. They rarely produce sticks or wood as they despawn.