This points to a problem in the DSLR viewfinder AF path, not the lens. Since Live View AF still works, the imaging sensor and lens communication are likely OK. The likely cause is the secondary mirror not returning fully to its correct position after the shutter cycle. When that happens, the dedicated AF sensor below the mirror box doesn’t get the proper light, so the camera just hunts and never achieves focus through the viewfinder. In the reported case, inspection found a broken hinge on the secondary mirror. If you’re repairing it yourself, inspect the main/secondary mirror mechanism and linkage carefully; damage or misalignment there can cause exactly this behavior.