Here in Texas, you need to bring potted lime trees inside/garage when temperatures drop much below 50°F and ensure the soil does not get bone dry and that the humidity levels in the room are not low. Keep the container away from direct hot/cold air vents. Expect some leaves to turn yellow and drop in winter. If the leaves are showing symptoms of interveinal leaf yellowing, consider acidifying the soil with garden sulfur; re-apply per product directions.
