Answer: Based on your description I am not certain what is happening with your lime tree. It should be evergreen with leaves all year. You can check to see if it is alive. Live wood is supple or flexible and has green inside the bark. Dead wood will be brittle and snap in your fingers, off-color brown or gray, and has no green inside the bark. Begin at the branch tips and trim off any dead wood.
If the tree is still alive, it should regrow with good care. Here are some tips to growing container citrus to help you trouble shoot. You may need to cut and paste the complete url into your browser to make it work correctly.
I hope your tree recovers.
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