Yellow leaves on lime tree in pot on patio Leander Tx

Not surprising its winter

Can you post photos? Is it an outdoor patio with sun?

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.

We have our citrus in the ground here so it goes all the way to the 30's if to has to. But lows below 50 are unavoidable and do not affect the trees at all.It really doesn't care. It rains enough to keep it happy in winter, our winters have actually trended toward wetter in recent years. I'm not sure what you do differently for potted plants. The fruit here is ripening now and people are harvesting