A lift chair hides a heavy steel lift mechanism inside what looks like an ordinary recliner, and that mechanism, not the upholstery, is what a mover needs to respect. Unplug it, secure it closed, and never lift it by the footrest.
Pro tip: Photograph the remote's cable routing into the chair base before disconnecting anything, since the connector and cable path is often not obvious once the chair is tipped for moving.
Watch out: Never lift or carry a lift chair by its footrest or arms; these attach to the lift mechanism, not the load-bearing frame, and can bend or detach under the chair's full weight.