Inside Oxford, the city's Building division reviews residential permit applications, issues permits and inspects remodels and alterations. Out in the county, Lafayette County requires a building permit for residential structures in subdivisions. Whether a lift needs a permit at your address isn't something I'd guess at, so we check with the office that covers it before work starts. When a job needs one, we handle the paperwork and line up the inspections.
Soil data rates Lafayette County's risk as real but uneven, with trouble concentrated on lots that drain poorly, lots that were cut and filled when they were graded, and houses with old plumbing leaking underneath. That matches what I see on jobs around here. The house that settled is usually the one with water around it or under it, not the one next door.
If your house sits in a Special Flood Hazard Area, the state's list of local floodplain activities includes substantial improvement assessments, so that's part of what we ask about when we check on the permit. We're based in Oxford and work across Lafayette County and the cities around it, including Batesville, Holly Springs and Pontotoc.