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I don't have much more information but I can get pictures in the morning once the sun's out.
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have you, or hired lawn chemical service, used any herbicides or weed killers inside the drip line of the tree, including if any being applied on lawn grass within or near the drip line? seize from doing that if so, and put in some fertilizer spikes around the edge of the drip line.
most common cause for ligustrum failing/dying is due to root rot. ligustrum become increasingly prone to root rot as they age; usually when the roots are constantly wet for too long of time, but drought, underwatering, or other stress can leave it more prone as well. they should be planted in location that drains well, and kept watered sufficiently (not too much and not too little). if specific limbs are affected due to root rot, you might prune them out and hope the tree recovers enough to grow new roots sufficiently that it recovers and delays the inevitable.