Lime trees are not tolerant of the cold and will suffer damage if the temperature should drop to below 50 degrees for several days in a row. Even in the Lower Rio Grande Valley, lime trees require winter protection, so if you want to grow then in North Texas, your best bet is to grow them in containers. This way you can bring the lime tree indoors prior to the onset of cold weather. Texas A&M University suggests growing either the Mexican or Tahiti lime in Texas. The Mexican lime tree, because it is smaller, is more suited to being grown in a container.
Plant the lime tree in an area that receives sun all day.
Remove all grass and weeds from within a 2-foot radius of the lime tree. If you must use herbicide, Texas A&M University suggests a systemic, contact herbicide be used, keeping it off the leaves and bark of the tree.
Water the lime tree every other day for the first month after planting, then decrease the watering interval to every 10 days. Water the tree slowly and deeply. If the tree is being grown in a container, allow the soil to dry and then water.
Fertilize the newly-planted lime tree with one cup of 21-0-0, split into three applications during the spring and summer. More mature lime trees should receive one cup of fertilizer for every year of the tree, split into applications in February, May and September. Always water prior to applying any fertilizer.
Protect the lime tree planted in the ground from winter frost by covering it completely with a tarp. Use holiday tree lights under the tarp for additional warmth.