There is a wide variety of plants that will do well growing under a lime tree. These are but a few examples. However, they all have features you need to look for, a love of shade, low-growing and easy to care for. Take a look, see what would fit your idea of a perfect companion plant for your lime tree and if it is not available in your area, there will be one similar.
Before deciding on a particular plant for under your lime tree, you need to take into consideration the fact that the plants and the tree are going to be competing for water and nutrients. They cannot just be left alone, no matter how strong and resilient they are. Also the roots are going to be competing for space.
Flowering Ground Covers
Aster '"Eastern Star" grows to a height of 24 inches, a width of 3 feet and produces a blanket of daisy like flowers that turn from white to rose to burgundy. Aster "Eastern Star" is hardy in zones 3 to 8. Barrenwort "Frohnleiten" will grow yellow flowers from zones 5 to 8 and, north of 5, it will be an evergreen.
Green Ground Covers
Bugleweed "Leprechaun" is a low-growing, shade-loving evergreen that is very easy to grow and only reaches 5 inches in height. Bugleweed "Leprechaun" is hardy in zones 3 to 9. Bethlehem Sage "Diana Clare" has silvery green leaves that grows up to 10 inches tall and 18 inches wide and is hardy in zones 4 to 8.
Bethlehem Sage "Raspberry Splash" produces clumps of raspberry-coloured flowers and is resistant to disease. After the flowers are gone, the leaves will make a spectacular display of their own. It grows to 12 inches in height, 24 inches in width and is hardy in zones 4 to 9. Eared Lady Fernchanges colours from purple and white to maroon and green. It grows 18 inches high and 24 inches wide and is hardy in zones 4 to 9. Heuchera "Melting Fire" is another easy-to-care for choice. The red/purple colours stay year-round. It grows to a height of 10 inches and a width of 12 and is hardy in zones 4 to 9.
St. Augustine Grass is one of the best for subtropical climates and does well in the shade. It can not tolerate high traffic, so under a lime tree is perfect. Try a variety like Bitter-Blue, which has a slow growth rate. It is a grass and will need to be cut.