
Usually, if the repair is designed around the tree rather than through it. Options in rough order of tree-friendliness: grind the lifted lip and leave the root; replace only the affected panels and ramp or bridge the concrete over the root; reroute the walk; or root-prune, but only well outside the anchorage zone — many arborists will not sever structural roots within a distance of several trunk diameters from the stem. Get the arborist and the concrete contractor on site together before anything is sawn. A demo crew cuts whatever is in the way, and nobody connects it to the tree that fails two years later.
Watch. The lift advances at the tree's growth rate — a fraction of an inch a year on a mature tree — so nothing about the tree becomes dangerous while you decide. What does change is the liability: the trip lip gets taller, and where the walk is public sidewalk, maintenance responsibility often falls to the adjoining property owner (this varies by municipality and is UNVERIFIED for your address — confirm with your city). Separately, water in the crack plus freeze-thaw will break the slab further each winter faster than the root will.