01 lesabre custom fuel gauge says full but hardly any gas is in then says empty

Hello, the fuel level being erroneous is due to either a faulty fuel sending unit (with the fuel pump in the fuel tank), a wiring issue to the sending unit, or a gauge issue. Testing specific to this system is required to find out what's going on. As far as riding rough - either a fuel delivery, ignition spark or air intake concern is present and needs troubleshooting performed to isolate to the cause. Good luck!