Prune out any dead or dying branches. If infection has reached the trunk, the tree cannot be saved. Avoid heavy fertilizing, but provide moderate amounts of slow-release fertilizer to keep plants healthy. Irrigation should be deep and infrequent. In the long run, the best solution is to plant resistant species.
Winters are too chilly for lime which is the least cold-tolerant of the citrus.
Mandarin would be a better choice. In any case, citrus will have to be protected from a serious or prolonged frost. In the spring, you may see the disk-shaped white eggs which are laid on fruit or nearby leaves. Hatching of eggs can be predicted using degree day calculations, which is important when timing treatment with BT or pesticide. 53-7 describes in detail various controls and their effectiveness.