my lime tree branches are being eaten by something– chewed off.
My lime tree branches are slowly being eaten -- they are perfectly being cut off.
Certified GKH Gardening Expert
Hm... If this is a perfect cut, then I would suspect foul play. Insects and animals will not leave straight lines as a knife or cutting utensil will.
Unless you catch what is responsible, or see signs of it, it will be very hard to say what is getting at your tree.
Here is an article that will help you with their care, though: https://www.gardeningknowhow.com/edible/fruits/lime/lime-tree-tips-care-of-lime-trees.htm