The existing FAA Airworthiness Directive (AD) identifies existing flight crew procedures to be used in those circumstances. The FAA and Boeing continue to evaluate the need for software and/or other design changes to the aircraft including operating procedures and training as we learn more from the ongoing investigation.The FAA is not doing a safety probe separate from the ongoing Lion Air Accident investigation of which we, the NTSB and Indonesian officials are a part.
Source: FAAFAA Statement on Boeing Model 737-8 and -9 Airplanes