Lemons and limes can be grown on the same tree. This is done by grafting a part from a lemon tree, called a scion, to a lime tree that acts as root stock. Once the tree accepts the scion, the branch will grow to bear fruit just like the tree it came from. In fact, citrus trees can bear branches with many kinds of fruit including orange, lemon, lime, tangerine, and grapefruit. A lemon scion can be grafted onto a lime tree using a technique called "T" budding with a fairly high rate of success.
Collect a branch with buds, called a budstick, from the desired lemon tree in the late winter, while the buds are dormant. The budstick should be mature growth from the previous season and up to 1/2 inch in diameter.
Cut the budstick with the pruning shears and remove any leaves. Wrap the budstick in a damp paper towel to keep it moist. Place it in a plastic bag and store it in the refrigerator until spring.
Do your budding in the spring as the buds on the lime tree acting as root stock are beginning to sprout.
Take a bud to be grafted from the budstick by slicing under the bud, starting about 1/2 inch below the base of the bud and ending 1/2 inch above it. Trim the top edge of the bud's bark square to form a little shield shape.
Remove the inner wood from under the bark of the bud by gently squeezing the bud, until the wood comes loose. Do not let the newly removed bud dry out.
Make a "T"-shaped cut through the bark of a one of the larger branches on a young lime tree. Do not cut too deeply. Lift the corners of the cut with the tip of the knife to loosen the bark from the trunk.
Slide the pointed part of the lemon bud's bark into the T cut so the bark is under the lime tree's bark. Insert the bud until the top of the shield meets the cross cut in the T.
Wrap the trunk with rubber band strips to hold the lemon bud in place. Do not cover the bud.
Check the bud after two weeks to see if the graft has taken. As the bud starts to grow, cut off the lime tree branch above it. From this point on, the new growth on that branch will bear lemons instead of limes.