My neighbor redid their driveway and now our lime tree is slowly dying. They must have cut a root unintentionally. What is the Halacha on them or us for them killing our tree?
My understanding of your question is two-fold. You mean to ask regarding the monetary aspect, and regarding the prohibition and kabalistic danger of cutting down a fruit tree.
Regarding the monetary aspect, you don’t know that he cut some of the roots of your tree, you are only making an assumption, that since the tree started dying after he redid his driveway, he must have cut some roots. This is not sufficient reason to force him to pay you for any damage.
Regarding the cutting the roots of the tree, assuming that the person got a contractor to redo his driveway, even if the roots were cut, they were done unintentionally by a gentile, and therefore in retrospect, the person would not have worry about any danger that might befall him as a result. Although there is controversy regarding using a gentile to cut down a fruit tree, post facto, if it was already done, especially in this scenario, when it isn’t even clear if that is what is hurting the tree, the person would not have to be concerned about it.